<!DOCTYPE html>
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<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1">
  <title>Unit Circle Solutions for sin θ = 1/2</title>
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</head>
<body>

<div class="main-wrap">
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    <text x="382" y="196" font-size="14" font-weight="600" fill="#64748b" class="math-txt">x</text>
    <text x="206" y="24" font-size="14" font-weight="600" fill="#64748b" class="math-txt">y</text>

    
    <circle cx="200" cy="200" r="140" fill="none" stroke="#334155" stroke-width="2.2" />

    
    
    <path id="arc-q1" d="M 242 200 A 42 42 0 0 0 236.37 179" fill="none" stroke="#f59e0b" stroke-width="2.5"/>
    <text id="lbl-ref-q1" x="256" y="188" font-size="13" font-weight="700" fill="#b45309" class="math-txt">π/6</text>

    
    <path id="arc-q2" d="M 158 200 A 42 42 0 0 1 163.63 179" fill="none" stroke="#f59e0b" stroke-width="2.5"/>
    <text id="lbl-ref-q2" x="132" y="188" font-size="13" font-weight="700" fill="#b45309" class="math-txt">π/6</text>

    
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      <text x="278" y="123" font-size="13" font-weight="700" fill="#1d4ed8" text-anchor="middle" class="math-txt">y = 1/2</text>
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      <text x="346" y="112" font-size="13" font-weight="700" fill="#ffffff" text-anchor="middle" class="math-txt">θ = π/6</text>
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      <circle cx="78.76" cy="130" r="6" fill="#0f766e" stroke="#ffffff" stroke-width="2"/>
      <rect x="20" y="96" width="76" height="24" rx="6" fill="#0f766e"/>
      <text x="58" y="112" font-size="13" font-weight="700" fill="#ffffff" text-anchor="middle" class="math-txt">θ = 5π/6</text>
    </g>
  </svg>

  
  <div class="btn-group">
    <button class="pill active" onclick="setMode('all')">Full View</button>
    <button class="pill" onclick="setMode('line')">y = 1/2 Line</button>
    <button class="pill" onclick="setMode('solutions')">2 Solutions</button>
    <button class="pill" onclick="setMode('ref')">Ref Angles</button>
  </div>
</div>

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</body>
</html>

Finding All Solutions to Trigonometric Equations on the Unit Circle

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      background: #f8fafc;
      color: #1e293b;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      height: 100%;
      padding: 12px;
      user-select: none;
    }

    .controls-row {
      display: flex;
      flex-wrap: wrap;
      justify-content: center;
      gap: 8px;
      width: 100%;
      z-index: 10;
    }

    .btn {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      border-radius: 6px;
      padding: 6px 12px;
      font-size: 13px;
      font-weight: 600;
      color: #475569;
      cursor: pointer;
      box-shadow: 0 1px 2px rgba(0,0,0,0.05);
      transition: all 0.2s ease;
    }
    .btn:hover {
      background: #f1f5f9;
      color: #0f172a;
    }
    .btn.active {
      background: #0284c7;
      border-color: #0284c7;
      color: #ffffff;
      box-shadow: 0 0 0 2px rgba(2,132,199,0.25);
    }

    .k-selector {
      display: flex;
      align-items: center;
      gap: 4px;
      background: #e2e8f0;
      padding: 3px;
      border-radius: 8px;
    }

    .k-btn {
      background: transparent;
      border: none;
      border-radius: 5px;
      padding: 4px 10px;
      font-size: 13px;
      font-weight: 600;
      color: #475569;
      cursor: pointer;
      transition: all 0.15s ease;
    }
    .k-btn.active {
      background: #ffffff;
      color: #0284c7;
      box-shadow: 0 1px 3px rgba(0,0,0,0.1);
    }

    .svg-container {
      width: 100%;
      flex: 1;
      max-height: 380px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }

    .axis { stroke: #94a3b8; stroke-width: 1.5; }
    .grid-line { stroke: #e2e8f0; stroke-width: 1; stroke-dasharray: 4,4; }
    .tick-label { font-size: 11px; fill: #64748b; text-anchor: middle; font-weight: 500; }
    .val-label { font-size: 12px; font-weight: 700; text-anchor: middle; transition: fill 0.2s; }
  </style>
</head>
<body>

  
  <div class="controls-row">
    <button id="btnBase1" class="btn active" onclick="setBase(0)">θ = π/6 + 2kπ</button>
    <button id="btnBase2" class="btn" onclick="setBase(1)">θ = 5π/6 + 2kπ</button>
  </div>

  
  <div class="svg-container">
    <svg viewBox="0 0 600 340">
      <defs>
        <marker id="arrow" viewBox="0 0 10 10" refX="5" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
          <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#0284c7"/>
        </marker>
        <marker id="arrow-period" viewBox="0 0 10 10" refX="5" refY="5" markerWidth="5" markerHeight="5" orient="auto-start-reverse">
          <path d="M 0 2 L 6 5 L 0 8 z" fill="#059669"/>
        </marker>
      </defs>

      
      <g transform="translate(300, 105)">
        
        <line x1="-95" y1="0" x2="95" y2="0" class="axis" />
        <line x1="0" y1="-85" x2="0" y2="85" class="axis" />

        
        <circle cx="0" cy="0" r="70" fill="none" stroke="#cbd5e1" stroke-width="2" />

        
        <line x1="-85" y1="-35" x2="85" y2="-35" stroke="#f59e0b" stroke-width="1.5" stroke-dasharray="3,3" />
        <text x="92" y="-31" font-size="11" fill="#d97706" font-weight="600">sin θ = ½</text>

        
        <path id="spiralPath" fill="none" stroke="#38bdf8" stroke-width="2" opacity="0.7" />

        
        <line id="vectorArm" x1="0" y1="0" x2="60.6" y2="-35" stroke="#0284c7" stroke-width="3" stroke-linecap="round" />
        <circle id="circlePoint" cx="60.6" cy="-35" r="5" fill="#0284c7" />

        
        <g id="angleBadge" transform="translate(0, 75)">
          <rect x="-45" y="-12" width="90" height="22" rx="4" fill="#f1f5f9" stroke="#cbd5e1" />
          <text id="angleText" x="0" y="3" font-size="11" font-weight="700" fill="#0369a1" text-anchor="middle">θ = π/6</text>
        </g>
      </g>

      
      <path id="dropGuide" stroke="#0284c7" stroke-width="1.5" stroke-dasharray="3,3" fill="none" opacity="0.6" />

      
      <g transform="translate(0, 260)">
        
        <line x1="30" y1="0" x2="570" y2="0" class="axis" stroke-width="2" />
        <polygon points="575,0 567,-4 567,4" fill="#94a3b8" />
        <polygon points="25,0 33,-4 33,4" fill="#94a3b8" />

        
        
        
        <g id="axisTicks">
          <line x1="140" y1="-6" x2="140" y2="6" class="axis" />
          <text x="140" y="20" class="tick-label">-2π</text>

          <line x1="190" y1="-4" x2="190" y2="4" class="axis" />
          <text x="190" y="20" class="tick-label">-π</text>

          <line x1="240" y1="-6" x2="240" y2="6" class="axis" stroke-width="2" />
          <text x="240" y="20" class="tick-label" font-weight="700">0</text>

          <line x1="290" y1="-4" x2="290" y2="4" class="axis" />
          <text x="290" y="20" class="tick-label">π</text>

          <line x1="340" y1="-6" x2="340" y2="6" class="axis" />
          <text x="340" y="20" class="tick-label">2π</text>

          <line x1="390" y1="-4" x2="390" y2="4" class="axis" />
          <text x="390" y="20" class="tick-label">3π</text>

          <line x1="440" y1="-6" x2="440" y2="6" class="axis" />
          <text x="440" y="20" class="tick-label">4π</text>

          <line x1="490" y1="-4" x2="490" y2="4" class="axis" />
          <text x="490" y="20" class="tick-label">5π</text>
        </g>

        
        <g id="periodArcGroup">
          <path id="periodArc" fill="none" stroke="#059669" stroke-width="1.5" marker-end="url(#arrow-period)" />
          <text id="periodText" y="-38" font-size="11" font-weight="700" fill="#059669" text-anchor="middle">Period T = 2π</text>
        </g>

        
        
        <g class="sol-node" onclick="setK(-1)" style="cursor:pointer">
          <circle id="dot_m1" cx="0" cy="0" r="5" fill="#cbd5e1" stroke="#ffffff" stroke-width="1.5" />
          <text id="label_m1" y="-12" class="val-label" fill="#64748b">-11π/6</text>
        </g>
        
        <g class="sol-node" onclick="setK(0)" style="cursor:pointer">
          <circle id="dot_0" cx="0" cy="0" r="5" fill="#cbd5e1" stroke="#ffffff" stroke-width="1.5" />
          <text id="label_0" y="-12" class="val-label" fill="#64748b">π/6</text>
        </g>
        
        <g class="sol-node" onclick="setK(1)" style="cursor:pointer">
          <circle id="dot_1" cx="0" cy="0" r="5" fill="#cbd5e1" stroke="#ffffff" stroke-width="1.5" />
          <text id="label_1" y="-12" class="val-label" fill="#64748b">13π/6</text>
        </g>
        
        <g class="sol-node" onclick="setK(2)" style="cursor:pointer">
          <circle id="dot_2" cx="0" cy="0" r="5" fill="#cbd5e1" stroke="#ffffff" stroke-width="1.5" />
          <text id="label_2" y="-12" class="val-label" fill="#64748b">25π/6</text>
        </g>

        
        <circle id="activeIndicator" cx="0" cy="0" r="9" fill="none" stroke="#0284c7" stroke-width="2.5" />
      </g>
    </svg>
  </div>

  
  <div class="controls-row">
    <div class="k-selector">
      <button id="kbtn_m1" class="k-btn" onclick="setK(-1)">k = -1</button>
      <button id="kbtn_0" class="k-btn active" onclick="setK(0)">k = 0</button>
      <button id="kbtn_1" class="k-btn" onclick="setK(1)">k = 1</button>
      <button id="kbtn_2" class="k-btn" onclick="setK(2)">k = 2</button>
    </div>
    <button id="playBtn" class="btn" onclick="toggleAutoPlay()">▶ Auto</button>
  </div>

  <script>
    // Geometry & Math definitions
    // Number line scale: 0 is at x = 240, scale is 50px per PI rad
    const X_ZERO = 240;
    const PI_SCALE = 50 / Math.PI; // px per radian => PI radians = 50px

    const CONFIGS = [
      {
        name: "pi6",
        baseRad: Math.PI / 6,
        labels: { "-1": "-11π/6", "0": "π/6", "1": "13π/6", "2": "25π/6" },
        dispLabels: { "-1": "θ = π/6 - 2π", "0": "θ = π/6", "1": "θ = π/6 + 2π", "2": "θ = π/6 + 4π" }
      },
      {
        name: "5pi6",
        baseRad: 5 * Math.PI / 6,
        labels: { "-1": "-7π/6", "0": "5π/6", "1": "17π/6", "2": "29π/6" },
        dispLabels: { "-1": "θ = 5π/6 - 2π", "0": "θ = 5π/6", "1": "θ = 5π/6 + 2π", "2": "θ = 5π/6 + 4π" }
      }
    ];

    let currentBase = 0;
    let currentK = 0;
    let autoInterval = null;

    function radToX(rad) {
      return X_ZERO + rad * PI_SCALE;
    }

    function update() {
      const cfg = CONFIGS[currentBase];
      const baseAngle = cfg.baseRad;
      const totalAngle = baseAngle + currentK * 2 * Math.PI;

      // 1. Circle Vector position
      const R = 70;
      const cx = R * Math.cos(baseAngle);
      const cy = -R * Math.sin(baseAngle); // SVG y is inverted

      const vectorArm = document.getElementById("vectorArm");
      const circlePoint = document.getElementById("circlePoint");
      vectorArm.setAttribute("x2", cx);
      vectorArm.setAttribute("y2", cy);
      circlePoint.setAttribute("cx", cx);
      circlePoint.setAttribute("cy", cy);

      // Spiral trace showing number of turns
      const spiralPath = document.getElementById("spiralPath");
      let pathD = "M 0 0 ";
      const turns = Math.abs(totalAngle);
      const steps = 60;
      const dir = totalAngle >= 0 ? 1 : -1;
      for (let i = 1; i <= steps; i++) {
        const a = dir * (i / steps) * turns;
        const r = Math.min(25, (i / steps) * 25);
        const sx = r * Math.cos(a);
        const sy = -r * Math.sin(a);
        pathD += `L ${sx.toFixed(1)} ${sy.toFixed(1)} `;
      }
      spiralPath.setAttribute("d", turns > 0.01 ? pathD : "");

      // Angle display badge
      document.getElementById("angleText").textContent = cfg.dispLabels[currentK];

      // 2. Number Line Dots Positions & Labels
      const kList = [-1, 0, 1, 2];
      kList.forEach(k => {
        const radVal = baseAngle + k * 2 * Math.PI;
        const xPos = radToX(radVal);
        const dot = document.getElementById(`dot_${k === -1 ? 'm1' : k}`);
        const label = document.getElementById(`label_${k === -1 ? 'm1' : k}`);
        
        dot.setAttribute("cx", xPos);
        label.setAttribute("x", xPos);
        label.textContent = cfg.labels[k];

        if (k === currentK) {
          dot.setAttribute("fill", "#0284c7");
          label.setAttribute("fill", "#0284c7");
          label.setAttribute("font-weight", "800");
        } else {
          dot.setAttribute("fill", "#94a3b8");
          label.setAttribute("fill", "#64748b");
          label.setAttribute("font-weight", "600");
        }
      });

      // Active Indicator
      const activeX = radToX(totalAngle);
      document.getElementById("activeIndicator").setAttribute("cx", activeX);

      // 3. Drop guide line from circle point (in root SVG coords: circle center is 300, 105)
      const rootCircleX = 300 + cx;
      const rootCircleY = 105 + cy;
      const rootTargetX = activeX;
      const rootTargetY = 260; // number line y in root SVG

      // Smooth curved path to drop
      const dropD = `M ${rootCircleX} ${rootCircleY} C ${rootCircleX} ${(rootCircleY + rootTargetY) / 2}, ${rootTargetX} ${(rootCircleY + rootTargetY) / 2}, ${rootTargetX} ${rootTargetY}`;
      document.getElementById("dropGuide").setAttribute("d", dropD);

      // 4. Period Arc (k=0 to k=1)
      const x0 = radToX(baseAngle);
      const x1 = radToX(baseAngle + 2 * Math.PI);
      const midX = (x0 + x1) / 2;
      const arcD = `M ${x0 + 4} -16 Q ${midX} -34 ${x1 - 4} -16`;
      document.getElementById("periodArc").setAttribute("d", arcD);
      document.getElementById("periodText").setAttribute("x", midX);

      // 5. Update UI active buttons
      document.getElementById("btnBase1").className = currentBase === 0 ? "btn active" : "btn";
      document.getElementById("btnBase2").className = currentBase === 1 ? "btn active" : "btn";

      kList.forEach(k => {
        const btn = document.getElementById(`kbtn_${k === -1 ? 'm1' : k}`);
        btn.className = k === currentK ? "k-btn active" : "k-btn";
      });
    }

    function setBase(idx) {
      currentBase = idx;
      update();
    }

    function setK(k) {
      currentK = k;
      update();
    }

    function toggleAutoPlay() {
      const playBtn = document.getElementById("playBtn");
      if (autoInterval) {
        clearInterval(autoInterval);
        autoInterval = null;
        playBtn.textContent = "▶ Auto";
        playBtn.classList.remove("active");
      } else {
        playBtn.textContent = "⏸ Pause";
        playBtn.classList.add("active");
        autoInterval = setInterval(() => {
          currentK = currentK >= 2 ? -1 : currentK + 1;
          update();
        }, 1500);
      }
    }

    // Initial render
    update();
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="1:1.15">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; font-family: system-ui, -apple-system, sans-serif; }
    body {
      background: #ffffff;
      color: #1e293b;
      display: flex;
      flex-direction: column;
      align-items: center;
      padding: 8px 10px;
      user-select: none;
    }
    .controls {
      width: 100%;
      max-width: 360px;
      display: flex;
      flex-direction: column;
      gap: 6px;
    }
    .btn-group {
      display: flex;
      background: #f1f5f9;
      border-radius: 8px;
      padding: 2px;
      gap: 2px;
    }
    .toggle-btn {
      flex: 1;
      padding: 6px 10px;
      font-size: 13px;
      font-weight: 600;
      border: none;
      background: transparent;
      color: #64748b;
      cursor: pointer;
      border-radius: 6px;
      transition: background 0.15s ease, color 0.15s ease;
      text-align: center;
    }
    .toggle-btn.active.sin {
      background: #059669;
      color: #ffffff;
    }
    .toggle-btn.active.cos {
      background: #2563eb;
      color: #ffffff;
    }
    .slider-row {
      display: flex;
      align-items: center;
      gap: 8px;
      background: #f8fafc;
      padding: 5px 10px;
      border-radius: 8px;
      border: 1px solid #e2e8f0;
    }
    .slider-label {
      font-size: 13px;
      font-weight: 700;
      min-width: 70px;
    }
    .slider {
      flex: 1;
      height: 6px;
      border-radius: 3px;
      accent-color: #059669;
      cursor: pointer;
    }
    .presets {
      display: flex;
      gap: 4px;
      justify-content: center;
      flex-wrap: wrap;
    }
    .preset-btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 4px;
      padding: 2px 7px;
      font-size: 11.5px;
      font-weight: 600;
      color: #334155;
      cursor: pointer;
      transition: background 0.15s ease;
    }
    .preset-btn:hover {
      background: #e2e8f0;
    }
    .svg-container {
      width: 100%;
      max-width: 360px;
      display: flex;
      justify-content: center;
      align-items: center;
      margin-top: 4px;
    }
    svg {
      width: 100%;
      height: auto;
      overflow: visible;
    }
    .solution-badge {
      margin-top: 4px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 6px 10px;
      font-size: 12.5px;
      font-weight: 600;
      text-align: center;
      width: 100%;
      max-width: 360px;
    }
    .text-sin { color: #059669; }
    .text-cos { color: #2563eb; }
    .text-ang { color: #d97706; }
    
    .point-badge-text {
      font-size: 10px;
      font-weight: 700;
      paint-order: stroke fill;
      stroke: #ffffff;
      stroke-width: 2.5px;
      stroke-linejoin: round;
    }
  </style>
</head>
<body>
  <div class="controls">
    <div class="btn-group">
      <button id="btnSin" class="toggle-btn active sin" onclick="setMode('sin')">sin(θ) = c</button>
      <button id="btnCos" class="toggle-btn cos" onclick="setMode('cos')">cos(θ) = c</button>
    </div>

    <div class="slider-row">
      <span id="sliderLabel" class="slider-label text-sin">c = 0.50</span>
      <input type="range" id="cSlider" class="slider" min="-100" max="100" value="50" oninput="onSlider(this.value)">
    </div>

    <div class="presets">
      <button class="preset-btn" onclick="setVal(-0.866)">-√3/2</button>
      <button class="preset-btn" onclick="setVal(-0.5)">-1/2</button>
      <button class="preset-btn" onclick="setVal(0)">0</button>
      <button class="preset-btn" onclick="setVal(0.5)">1/2</button>
      <button class="preset-btn" onclick="setVal(0.707)">√2/2</button>
      <button class="preset-btn" onclick="setVal(0.866)">√3/2</button>
      <button class="preset-btn" onclick="setVal(1)">1</button>
    </div>
  </div>

  <div class="svg-container">
    <svg viewBox="0 0 360 360" id="circleSvg">
      <defs>
        <filter id="glow" x="-30%" y="-30%" width="160%" height="160%">
          <feGaussianBlur stdDeviation="2.5" result="blur" />
          <feComposite in="SourceGraphic" in2="blur" operator="over" />
        </filter>
        <filter id="badgeShadow" x="-20%" y="-20%" width="140%" height="140%">
          <feDropShadow dx="0" dy="1" stdDeviation="1.5" flood-color="#000000" flood-opacity="0.15" />
        </filter>
      </defs>

      
      <g id="angleGrid" stroke="#e2e8f0" stroke-width="1"></g>

      
      <line x1="15" y1="180" x2="345" y2="180" stroke="#94a3b8" stroke-width="1.2" />
      <line x1="180" y1="15" x2="180" y2="345" stroke="#94a3b8" stroke-width="1.2" />
      
      
      <text x="350" y="184" font-size="12" fill="#64748b" font-weight="700">x</text>
      <text x="180" y="11" font-size="12" fill="#64748b" font-weight="700" text-anchor="middle">y</text>
      
      
      <g id="radianLabels" font-size="10.5" font-weight="600" fill="#475569" text-anchor="middle" dominant-baseline="central"></g>

      
      <circle cx="180" cy="180" r="112" fill="none" stroke="#64748b" stroke-width="1.8" />

      
      <path id="arc1" fill="rgba(245, 158, 11, 0.15)" stroke="#d97706" stroke-width="1.5" />
      <path id="arc2" fill="rgba(245, 158, 11, 0.15)" stroke="#d97706" stroke-width="1.5" stroke-dasharray="3 2" />
      <line id="ray1" x1="180" y1="180" x2="180" y2="180" stroke="#d97706" stroke-width="1.5" />
      <line id="ray2" x1="180" y1="180" x2="180" y2="180" stroke="#d97706" stroke-width="1.5" />

      
      <line id="cutLine" stroke="#059669" stroke-width="2" stroke-dasharray="4 3" />
      <rect id="cutLineLabelBg" rx="3" ry="3" fill="#ffffff" fill-opacity="0.9" stroke="#cbd5e1" stroke-width="0.8" />
      <text id="cutLineLabel" font-size="11" font-weight="700" fill="#059669" dominant-baseline="central"></text>

      
      <circle id="pt1" r="5.5" fill="#059669" stroke="#ffffff" stroke-width="2" filter="url(#glow)" />
      <circle id="pt2" r="5.5" fill="#059669" stroke="#ffffff" stroke-width="2" filter="url(#glow)" />

      
      <g id="badgeGroup1" filter="url(#badgeShadow)">
        <rect id="bgPt1" rx="4" ry="4" fill="#ffffff" stroke="#059669" stroke-width="1.2" />
        <text id="lblPt1" class="point-badge-text" fill="#0f172a" text-anchor="middle" dominant-baseline="central"></text>
      </g>

      
      <g id="badgeGroup2" filter="url(#badgeShadow)">
        <rect id="bgPt2" rx="4" ry="4" fill="#ffffff" stroke="#059669" stroke-width="1.2" />
        <text id="lblPt2" class="point-badge-text" fill="#0f172a" text-anchor="middle" dominant-baseline="central"></text>
      </g>
    </svg>
  </div>

  <div id="solutionBadge" class="solution-badge">
    Solutions: <span class="text-ang">θ₁ = π/6</span> &nbsp;|&nbsp; <span class="text-ang">θ₂ = 5π/6</span>
  </div>

  <script>
    const CX = 180, CY = 180, R = 112;
    let mode = 'sin';
    let cVal = 0.5;

    const stdAngles = [
      { r: 0, rad: "0" },
      { r: Math.PI / 6, rad: "π/6" },
      { r: Math.PI / 4, rad: "π/4" },
      { r: Math.PI / 3, rad: "π/3" },
      { r: Math.PI / 2, rad: "π/2" },
      { r: 2 * Math.PI / 3, rad: "2π/3" },
      { r: 3 * Math.PI / 4, rad: "3π/4" },
      { r: 5 * Math.PI / 6, rad: "5π/6" },
      { r: Math.PI, rad: "π" },
      { r: 7 * Math.PI / 6, rad: "7π/6" },
      { r: 5 * Math.PI / 4, rad: "5π/4" },
      { r: 4 * Math.PI / 3, rad: "4π/3" },
      { r: 3 * Math.PI / 2, rad: "3π/2" },
      { r: 5 * Math.PI / 3, rad: "5π/3" },
      { r: 7 * Math.PI / 4, rad: "7π/4" },
      { r: 11 * Math.PI / 6, rad: "11π/6" }
    ];

    function initStaticCircle() {
      const gGrid = document.getElementById('angleGrid');
      const gLabels = document.getElementById('radianLabels');
      
      stdAngles.forEach(a => {
        const cos = Math.cos(a.r);
        const sin = Math.sin(a.r);

        // Ray grid line
        const line = document.createElementNS("http://www.w3.org/2000/svg", "line");
        line.setAttribute("x1", CX);
        line.setAttribute("y1", CY);
        line.setAttribute("x2", CX + R * cos);
        line.setAttribute("y2", CY - R * sin);
        gGrid.appendChild(line);

        // Tick mark crossing circle
        const tick = document.createElementNS("http://www.w3.org/2000/svg", "line");
        tick.setAttribute("x1", CX + (R - 3) * cos);
        tick.setAttribute("y1", CY - (R - 3) * sin);
        tick.setAttribute("x2", CX + (R + 3) * cos);
        tick.setAttribute("y2", CY - (R + 3) * sin);
        tick.setAttribute("stroke", "#64748b");
        tick.setAttribute("stroke-width", "1.2");
        gGrid.appendChild(tick);

        // High contrast perimeter label
        const dist = 22;
        const lx = CX + (R + dist) * cos;
        const ly = CY - (R + dist) * sin;
        
        const txt = document.createElementNS("http://www.w3.org/2000/svg", "text");
        txt.setAttribute("x", lx);
        txt.setAttribute("y", ly);
        txt.textContent = a.rad;
        gLabels.appendChild(txt);
      });
    }

    function setMode(m) {
      mode = m;
      const isSin = mode === 'sin';
      document.getElementById('btnSin').className = 'toggle-btn ' + (isSin ? 'active sin' : 'sin');
      document.getElementById('btnCos').className = 'toggle-btn ' + (!isSin ? 'active cos' : 'cos');
      
      const slider = document.getElementById('cSlider');
      slider.style.accentColor = isSin ? '#059669' : '#2563eb';
      
      const label = document.getElementById('sliderLabel');
      label.className = 'slider-label ' + (isSin ? 'text-sin' : 'text-cos');
      
      update();
    }

    function setVal(v) {
      cVal = v;
      document.getElementById('cSlider').value = Math.round(v * 100);
      update();
    }

    function onSlider(v) {
      cVal = parseInt(v, 10) / 100;
      update();
    }

    function formatRad(rad) {
      const norm = (rad % (2 * Math.PI) + 2 * Math.PI) % (2 * Math.PI);
      for (const a of stdAngles) {
        if (Math.abs(norm - a.r) < 0.04) return a.rad;
      }
      return (norm / Math.PI).toFixed(2) + "π";
    }

    function formatVal(v) {
      if (Math.abs(v - 0.866) < 0.02) return "√3/2";
      if (Math.abs(v + 0.866) < 0.02) return "-√3/2";
      if (Math.abs(v - 0.707) < 0.02) return "√2/2";
      if (Math.abs(v + 0.707) < 0.02) return "-√2/2";
      if (Math.abs(v - 0.5) < 0.02) return "1/2";
      if (Math.abs(v + 0.5) < 0.02) return "-1/2";
      return v.toFixed(2);
    }

    function positionBadge(bgEl, txtEl, angle, px, py, textStr, strokeColor) {
      txtEl.textContent = textStr;
      bgEl.setAttribute('stroke', strokeColor);

      // Position badge inwards towards the circle center so it doesn't collide with perimeter radian labels
      const inwardDist = 38;
      const bx = CX + (R - inwardDist) * Math.cos(angle);
      const by = CY - (R - inwardDist) * Math.sin(angle);

      // Center text inside pill
      txtEl.setAttribute('x', bx);
      txtEl.setAttribute('y', by);

      // Sizing pill
      const pillWidth = textStr.length * 6.2 + 14;
      const pillHeight = 18;
      bgEl.setAttribute('x', bx - pillWidth / 2);
      bgEl.setAttribute('y', by - pillHeight / 2);
      bgEl.setAttribute('width', pillWidth);
      bgEl.setAttribute('height', pillHeight);
    }

    function update() {
      const color = mode === 'sin' ? '#059669' : '#2563eb';
      document.getElementById('sliderLabel').textContent = `c = ${formatVal(cVal)}`;

      const cutLine = document.getElementById('cutLine');
      const cutLabel = document.getElementById('cutLineLabel');
      const cutLabelBg = document.getElementById('cutLineLabelBg');
      const pt1 = document.getElementById('pt1');
      const pt2 = document.getElementById('pt2');
      const bgPt1 = document.getElementById('bgPt1');
      const bgPt2 = document.getElementById('bgPt2');
      const lblPt1 = document.getElementById('lblPt1');
      const lblPt2 = document.getElementById('lblPt2');
      const badgeGroup1 = document.getElementById('badgeGroup1');
      const badgeGroup2 = document.getElementById('badgeGroup2');
      const ray1 = document.getElementById('ray1');
      const ray2 = document.getElementById('ray2');
      const arc1 = document.getElementById('arc1');
      const arc2 = document.getElementById('arc2');

      cutLine.setAttribute('stroke', color);
      cutLabel.setAttribute('fill', color);
      pt1.setAttribute('fill', color);
      pt2.setAttribute('fill', color);

      let a1, a2, p1x, p1y, p2x, p2y;

      if (mode === 'sin') {
        const lineY = CY - cVal * R;
        cutLine.setAttribute('x1', 20);
        cutLine.setAttribute('y1', lineY);
        cutLine.setAttribute('x2', 340);
        cutLine.setAttribute('y2', lineY);
        
        const labelText = `y = ${formatVal(cVal)}`;
        cutLabel.textContent = labelText;
        const lx = 24;
        const ly = lineY > CY ? lineY - 10 : lineY + 10;
        cutLabel.setAttribute('x', lx + 4);
        cutLabel.setAttribute('y', ly);
        cutLabelBg.setAttribute('x', lx);
        cutLabelBg.setAttribute('y', ly - 8);
        cutLabelBg.setAttribute('width', labelText.length * 6.5 + 8);
        cutLabelBg.setAttribute('height', 16);

        const baseAngle = Math.asin(Math.max(-1, Math.min(1, cVal)));
        a1 = (baseAngle + 2 * Math.PI) % (2 * Math.PI);
        a2 = (Math.PI - baseAngle + 2 * Math.PI) % (2 * Math.PI);

        if (a1 > a2) { const tmp = a1; a1 = a2; a2 = tmp; }

        p1x = CX + R * Math.cos(a1);
        p1y = CY - R * Math.sin(a1);
        p2x = CX + R * Math.cos(a2);
        p2y = CY - R * Math.sin(a2);
      } else {
        const lineX = CX + cVal * R;
        cutLine.setAttribute('x1', lineX);
        cutLine.setAttribute('y1', 20);
        cutLine.setAttribute('x2', lineX);
        cutLine.setAttribute('y2', 340);

        const labelText = `x = ${formatVal(cVal)}`;
        cutLabel.textContent = labelText;
        const lx = lineX > CX ? lineX - 60 : lineX + 6;
        const ly = 25;
        cutLabel.setAttribute('x', lx + 4);
        cutLabel.setAttribute('y', ly);
        cutLabelBg.setAttribute('x', lx);
        cutLabelBg.setAttribute('y', ly - 8);
        cutLabelBg.setAttribute('width', labelText.length * 6.5 + 8);
        cutLabelBg.setAttribute('height', 16);

        const baseAngle = Math.acos(Math.max(-1, Math.min(1, cVal)));
        a1 = baseAngle;
        a2 = (2 * Math.PI - baseAngle) % (2 * Math.PI);

        if (a1 > a2) { const tmp = a1; a1 = a2; a2 = tmp; }

        p1x = CX + R * Math.cos(a1);
        p1y = CY - R * Math.sin(a1);
        p2x = CX + R * Math.cos(a2);
        p2y = CY - R * Math.sin(a2);
      }

      pt1.setAttribute('cx', p1x);
      pt1.setAttribute('cy', p1y);
      pt2.setAttribute('cx', p2x);
      pt2.setAttribute('cy', p2y);

      ray1.setAttribute('x2', p1x);
      ray1.setAttribute('y2', p1y);
      ray2.setAttribute('x2', p2x);
      ray2.setAttribute('y2', p2y);

      // Arc helper
      const rArc1 = 30;
      const rArc2 = 40;
      arc1.setAttribute('d', `M ${CX} ${CY} L ${CX + rArc1} ${CY} A ${rArc1} ${rArc1} 0 ${a1 > Math.PI ? 1 : 0} 0 ${CX + rArc1 * Math.cos(a1)} ${CY - rArc1 * Math.sin(a1)} Z`);
      arc2.setAttribute('d', `M ${CX} ${CY} L ${CX + rArc2} ${CY} A ${rArc2} ${rArc2} 0 ${a2 > Math.PI ? 1 : 0} 0 ${CX + rArc2 * Math.cos(a2)} ${CY - rArc2 * Math.sin(a2)} Z`);

      // Dynamic badges positioned cleanly to prevent overlap
      positionBadge(bgPt1, lblPt1, a1, p1x, p1y, `θ₁ = ${formatRad(a1)}`, color);

      const isSingle = Math.abs(a1 - a2) < 0.01;
      if (isSingle) {
        pt2.style.display = 'none';
        badgeGroup2.style.display = 'none';
        ray2.style.display = 'none';
        arc2.style.display = 'none';
        positionBadge(bgPt1, lblPt1, a1, p1x, p1y, `θ = ${formatRad(a1)}`, color);
      } else {
        pt2.style.display = '';
        badgeGroup2.style.display = '';
        ray2.style.display = '';
        arc2.style.display = '';
        positionBadge(bgPt2, lblPt2, a2, p2x, p2y, `θ₂ = ${formatRad(a2)}`, color);
      }

      // Bottom solution badge
      const badge = document.getElementById('solutionBadge');
      if (isSingle) {
        badge.innerHTML = `Single Solution in [0, 2π): <span class="text-ang">θ = ${formatRad(a1)}</span>`;
      } else {
        badge.innerHTML = `Solutions in [0, 2π): <span class="text-ang">θ₁ = ${formatRad(a1)}</span> &nbsp;|&nbsp; <span class="text-ang">θ₂ = ${formatRad(a2)}</span>`;
      }
    }

    initStaticCircle();
    update();
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      color: #1e2945;
      background: #ffffff;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 8px 12px;
      user-select: none;
    }

    .diagram-area {
      width: 100%;
      max-width: 600px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    /* SVG Graph */
    .graph-container {
      width: 100%;
      position: relative;
    }
    svg {
      width: 100%;
      height: auto;
      display: block;
      overflow: visible;
    }

    .grid-line {
      stroke: #e2e8f0;
      stroke-width: 1;
      stroke-dasharray: 3 3;
    }
    .axis-line {
      stroke: #94a3b8;
      stroke-width: 1.5;
    }
    .midline {
      stroke: #64748b;
      stroke-width: 1.2;
      stroke-dasharray: 4 4;
    }
    .curve {
      fill: none;
      stroke: #22b7ff;
      stroke-width: 3.5;
      stroke-linecap: round;
    }
    .curve-fill {
      fill: rgba(34, 183, 255, 0.12);
      stroke: none;
    }
    .axis-text {
      font-size: 11px;
      fill: #64748b;
      font-weight: 500;
    }
    .axis-title {
      font-size: 11px;
      fill: #1e2945;
      font-weight: 700;
    }

    /* Pulsing tide markers */
    .tide-marker {
      cursor: pointer;
      transition: transform 0.2s ease;
    }
    .pulse-ring {
      fill: none;
      stroke: #0284c7;
      stroke-width: 1.5;
      animation: pulse 2s infinite ease-out;
      transform-origin: center;
    }
    @keyframes pulse {
      0% { r: 5; opacity: 1; }
      100% { r: 14; opacity: 0; }
    }

    /* Harbor Cross-section */
    .harbor-panel {
      position: relative;
      width: 100%;
      height: 90px;
      background: #f1f5f9;
      border-radius: 8px;
      overflow: hidden;
      display: flex;
      border: 1px solid #cbd5e1;
    }
    .harbor-wall {
      width: 48px;
      height: 100%;
      background: repeating-linear-gradient(
        45deg,
        #94a3b8,
        #94a3b8 6px,
        #64748b 6px,
        #64748b 12px
      );
      border-right: 2px solid #475569;
      flex-shrink: 0;
      position: relative;
    }
    .harbor-basin {
      flex: 1;
      position: relative;
      background: #e2e8f0;
      overflow: hidden;
    }
    .harbor-water {
      position: absolute;
      bottom: 0;
      left: 0;
      right: 0;
      background: linear-gradient(180deg, #38bdf8 0%, #0284c7 100%);
      transition: height 0.05s linear;
    }
    .water-surface {
      position: absolute;
      top: 0;
      left: 0;
      right: 0;
      height: 4px;
      background: #bae6fd;
    }
    .boat {
      position: absolute;
      left: 50%;
      bottom: 100%;
      transform: translateX(-50%) translateY(6px);
      font-size: 24px;
      line-height: 1;
      filter: drop-shadow(0 2px 2px rgba(0,0,0,0.2));
      transition: bottom 0.05s linear;
    }
    .seabed {
      position: absolute;
      bottom: 0;
      left: 0;
      right: 0;
      height: 10px;
      background: #78716c;
      border-top: 2px solid #57534e;
    }
    .depth-badge {
      position: absolute;
      right: 10px;
      top: 8px;
      background: rgba(255, 255, 255, 0.95);
      border: 1px solid #cbd5e1;
      border-radius: 6px;
      padding: 4px 8px;
      font-size: 13px;
      font-weight: 700;
      color: #0369a1;
      box-shadow: 0 1px 3px rgba(0,0,0,0.05);
    }

    /* Controls */
    .controls {
      width: 100%;
      display: flex;
      align-items: center;
      gap: 10px;
    }
    .play-btn {
      background: #22b7ff;
      color: #fff;
      border: none;
      border-radius: 6px;
      padding: 6px 14px;
      font-size: 14px;
      font-weight: 600;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      min-width: 44px;
      height: 34px;
    }
    .play-btn:hover {
      background: #009be5;
    }
    .slider-wrap {
      flex: 1;
      display: flex;
      flex-direction: column;
      gap: 2px;
    }
    input[type=range] {
      width: 100%;
      accent-color: #0284c7;
      cursor: pointer;
      height: 6px;
    }
    .key-buttons {
      display: flex;
      justify-content: space-between;
      gap: 4px;
      width: 100%;
    }
    .tide-tag {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 4px;
      padding: 2px 6px;
      font-size: 11px;
      font-weight: 600;
      color: #1e2945;
      cursor: pointer;
    }
    .tide-tag:hover {
      background: #e2e8f0;
      border-color: #94a3b8;
    }
  </style>
</head>
<body>

  <div class="diagram-area">
    
    <div class="graph-container">
      <svg id="tideSvg" viewBox="0 0 540 220">
        
        <g id="grid"></g>
        
        
        <line id="midlinePath" class="midline" x1="45" x2="520" y1="97.7" y2="97.7" />
        <text x="522" y="101" font-size="10" fill="#64748b" font-weight="600">Midline 10 ft</text>

        
        <path id="curveArea" class="curve-fill" />
        <path id="curveLine" class="curve" />

        
        <line class="axis-line" x1="45" y1="190" x2="520" y2="190" />
        <line class="axis-line" x1="45" y1="15" x2="45" y2="190" />

        
        <text class="axis-title" x="270" y="215" text-anchor="middle">Time (hours)</text>
        <text class="axis-title" x="12" y="14" text-anchor="start">Depth (ft)</text>

        
        <g id="scrubberIndicator">
          <line id="trackLine" stroke="#0284c7" stroke-width="1.5" stroke-dasharray="2 2" y1="20" y2="190" />
          <circle id="trackDot" r="6" fill="#0284c7" stroke="#ffffff" stroke-width="2" />
        </g>

        
        <g id="tidePoints"></g>
      </svg>
    </div>

    
    <div class="harbor-panel">
      <div class="harbor-wall"></div>
      <div class="harbor-basin">
        <div id="harborWater" class="harbor-water" style="height: 55%;">
          <div class="water-surface"></div>
          <div class="boat">⛵</div>
        </div>
        <div class="seabed"></div>
        <div id="depthBadge" class="depth-badge">10.0 ft</div>
      </div>
    </div>

    
    <div class="controls">
      <button id="playBtn" class="play-btn" onclick="togglePlay()">▶</button>
      <div class="slider-wrap">
        <input type="range" id="timeSlider" min="0" max="24" step="0.1" value="4" oninput="onSliderMove(this.value)">
        <div class="key-buttons">
          <button class="tide-tag" onclick="jumpTo(4)">High: 4h (16ft)</button>
          <button class="tide-tag" onclick="jumpTo(10.2)">Low: 10.2h (4ft)</button>
          <button class="tide-tag" onclick="jumpTo(16.4)">High: 16.4h (16ft)</button>
          <button class="tide-tag" onclick="jumpTo(22.6)">Low: 22.6h (4ft)</button>
        </div>
      </div>
    </div>
  </div>

  <script>
    // Formula: y(t) = 6 * cos(pi/6.2 * (t - 4)) + 10
    const xMin = 0, xMax = 24;
    const yMin = 0, yMax = 18;
    const svgLeft = 45, svgRight = 515;
    const svgTop = 20, svgBottom = 190;

    function getX(t) {
      return svgLeft + (t - xMin) / (xMax - xMin) * (svgRight - svgLeft);
    }
    function getY(v) {
      return svgBottom - (v - yMin) / (yMax - yMin) * (svgBottom - svgTop);
    }
    function tideFunc(t) {
      return 6 * Math.cos((Math.PI / 6.2) * (t - 4)) + 10;
    }

    // Build Grid & Labels
    const gridG = document.getElementById('grid');
    for (let v = 0; v <= 18; v += 3) {
      const y = getY(v);
      gridG.innerHTML += `<line class="grid-line" x1="${svgLeft}" y1="${y}" x2="${svgRight}" y2="${y}"/>`;
      gridG.innerHTML += `<text class="axis-text" x="${svgLeft - 8}" y="${y + 4}" text-anchor="end">${v}</text>`;
    }
    for (let t = 0; t <= 24; t += 4) {
      const x = getX(t);
      gridG.innerHTML += `<line class="grid-line" x1="${x}" y1="${svgTop}" x2="${x}" y2="${svgBottom}"/>`;
      gridG.innerHTML += `<text class="axis-text" x="${x}" y="${svgBottom + 14}" text-anchor="middle">${t}h</text>`;
    }

    // Build Curve Path
    let pathD = "";
    let fillD = `M ${getX(0)} ${svgBottom} `;
    for (let t = 0; t <= 24.05; t += 0.1) {
      const x = getX(t);
      const y = getY(tideFunc(t));
      if (t === 0) {
        pathD += `M ${x} ${y} `;
        fillD += `L ${x} ${y} `;
      } else {
        pathD += `L ${x} ${y} `;
        fillD += `L ${x} ${y} `;
      }
    }
    fillD += `L ${getX(24)} ${svgBottom} Z`;
    document.getElementById('curveLine').setAttribute('d', pathD);
    document.getElementById('curveArea').setAttribute('d', fillD);

    // Key Tide Points
    const keyPoints = [
      { t: 4, name: "High Tide", depth: 16 },
      { t: 10.2, name: "Low Tide", depth: 4 },
      { t: 16.4, name: "High Tide", depth: 16 },
      { t: 22.6, name: "Low Tide", depth: 4 }
    ];

    const tidePointsG = document.getElementById('tidePoints');
    keyPoints.forEach(pt => {
      const px = getX(pt.t);
      const py = getY(pt.depth);
      const g = document.createElementNS('http://www.w3.org/2000/svg', 'g');
      g.setAttribute('class', 'tide-marker');
      g.onclick = () => jumpTo(pt.t);
      g.innerHTML = `
        <circle class="pulse-ring" cx="${px}" cy="${py}" r="6"/>
        <circle cx="${px}" cy="${py}" r="4.5" fill="#0284c7" stroke="#ffffff" stroke-width="1.5"/>
        <text x="${px}" y="${pt.depth === 16 ? py - 9 : py + 16}" font-size="10" font-weight="700" fill="#0369a1" text-anchor="middle">
          ${pt.depth === 16 ? 'High (16 ft)' : 'Low (4 ft)'}
        </text>
      `;
      tidePointsG.appendChild(g);
    });

    // Scrubber & Water Level Update
    const slider = document.getElementById('timeSlider');
    const trackLine = document.getElementById('trackLine');
    const trackDot = document.getElementById('trackDot');
    const harborWater = document.getElementById('harborWater');
    const depthBadge = document.getElementById('depthBadge');

    function updateState(t) {
      t = Math.max(0, Math.min(24, t));
      slider.value = t;
      const depth = tideFunc(t);
      const x = getX(t);
      const y = getY(depth);

      trackLine.setAttribute('x1', x);
      trackLine.setAttribute('x2', x);
      trackDot.setAttribute('cx', x);
      trackDot.setAttribute('cy', y);

      // Map depth (0 to 18 ft) to harbor basin height (10% to 90%)
      const waterPct = 10 + (depth / 18) * 80;
      harborWater.style.height = `${waterPct}%`;
      depthBadge.textContent = `${t.toFixed(1)}h: ${depth.toFixed(1)} ft`;
    }

    function onSliderMove(val) {
      if (isPlaying) togglePlay();
      updateState(parseFloat(val));
    }

    function jumpTo(t) {
      if (isPlaying) togglePlay();
      updateState(t);
    }

    // Auto Play Animation
    let isPlaying = false;
    let animInterval = null;
    const playBtn = document.getElementById('playBtn');

    function togglePlay() {
      isPlaying = !isPlaying;
      playBtn.textContent = isPlaying ? '⏸' : '▶';
      if (isPlaying) {
        animInterval = setInterval(() => {
          let nextT = parseFloat(slider.value) + 0.1;
          if (nextT > 24) nextT = 0;
          updateState(nextT);
        }, 50);
      } else {
        clearInterval(animInterval);
      }
    }

    // Initial state
    updateState(4);
  </script>
</body>
</html>

Modeling Tidal and Water Depth Cycles with Sinusoids

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px 16px;
      user-select: none;
    }

    .diagram-wrap {
      width: 100%;
      max-width: 580px;
      position: relative;
    }

    svg {
      width: 100%;
      height: auto;
      display: block;
      overflow: visible;
    }

    .axis-line { stroke: #94a3b8; stroke-width: 1.5; }
    .grid-line { stroke: #f1f5f9; stroke-width: 1; }
    .tick-text { font-size: 11px; fill: #64748b; font-weight: 500; }
    .label-text { font-size: 12px; font-weight: 600; }

    /* Interactive control */
    .controls {
      width: 100%;
      max-width: 580px;
      display: flex;
      align-items: center;
      gap: 12px;
      margin-top: 6px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 6px 12px;
    }

    .slider {
      flex: 1;
      height: 6px;
      accent-color: #0284c7;
      cursor: pointer;
    }

    .status-badge {
      font-size: 12px;
      font-weight: 700;
      padding: 3px 8px;
      border-radius: 6px;
      white-space: nowrap;
    }
    .status-safe { background: #dcfce7; color: #15803d; }
    .status-hazard { background: #fee2e2; color: #b91c1c; }
  </style>
</head>
<body>

  <div class="diagram-wrap">
    <svg id="chart" viewBox="0 0 560 340">
      <defs>
        
        <linearGradient id="safeGrad" x1="0" y1="0" x2="0" y2="1">
          <stop offset="0%" stop-color="#22c55e" stop-opacity="0.35"/>
          <stop offset="100%" stop-color="#22c55e" stop-opacity="0.1"/>
        </linearGradient>
        <linearGradient id="hazardGrad" x1="0" y1="0" x2="0" y2="1">
          <stop offset="0%" stop-color="#ef4444" stop-opacity="0.15"/>
          <stop offset="100%" stop-color="#ef4444" stop-opacity="0.05"/>
        </linearGradient>

        <marker id="arrow" viewBox="0 0 6 6" refX="3" refY="3" markerWidth="4" markerHeight="4" orient="auto-start-reverse">
          <path d="M 0 1.5 L 4.5 3 L 0 4.5 z" fill="#0284c7"/>
        </marker>
      </defs>

      
      <g id="gridLayer"></g>
      <path id="hazardArea" fill="url(#hazardGrad)"></path>
      <path id="safeArea" fill="url(#safeGrad)"></path>
      <line id="threshLine" stroke="#e11d48" stroke-width="1.75" stroke-dasharray="4,4"></line>
      <path id="curvePath" fill="none" stroke="#0284c7" stroke-width="3"></path>

      
      <g id="annotLayer">
        
        <rect x="420" y="112" width="105" height="20" rx="4" fill="#fff" stroke="#fda4af" stroke-width="1"/>
        <text x="472" y="126" text-anchor="middle" font-size="11" font-weight="700" fill="#e11d48">Draft: 13 ft</text>

        
        <rect x="230" y="98" width="100" height="20" rx="4" fill="#dcfce7" stroke="#86efac" stroke-width="1"/>
        <text x="280" y="112" text-anchor="middle" font-size="11" font-weight="700" fill="#15803d">Safe Window (≥13 ft)</text>

        
        <text x="75" y="240" font-size="12" font-weight="700" fill="#b91c1c">Hazard Zone (&lt;13 ft)</text>

        
        <circle id="peakDot" r="4.5" fill="#0284c7" stroke="#fff" stroke-width="1.5"></circle>
        <text x="280" y="32" text-anchor="middle" font-size="12" font-weight="700" fill="#0369a1">Peak: 4:00 AM (17 ft)</text>

        
        <line id="arrLeft" stroke="#0284c7" stroke-width="1.5" marker-end="url(#arrow)" marker-start="url(#arrow)"></line>
        <line id="arrRight" stroke="#0284c7" stroke-width="1.5" marker-end="url(#arrow)" marker-start="url(#arrow)"></line>
        
        <text id="txtLeft" text-anchor="middle" font-size="11" font-weight="600" fill="#0369a1"></text>
        <text id="txtRight" text-anchor="middle" font-size="11" font-weight="600" fill="#0369a1"></text>

        
        <line id="vGuide1" stroke="#22c55e" stroke-width="1" stroke-dasharray="3,3"></line>
        <line id="vGuide2" stroke="#22c55e" stroke-width="1" stroke-dasharray="3,3"></line>
      </g>

      
      <g id="tracker">
        <line id="trackLine" stroke="#64748b" stroke-width="1" stroke-dasharray="2,2"></line>
        <circle id="trackDot" r="6" fill="#0284c7" stroke="#fff" stroke-width="2"></circle>
        <text id="trackLabel" font-size="18" text-anchor="middle">⛵</text>
      </g>
    </svg>
  </div>

  
  <div class="controls">
    <span style="font-size: 12px; font-weight: 600; color: #475569;">Time:</span>
    <input type="range" id="timeSlider" class="slider" min="0" max="8" step="0.02" value="4">
    <div id="statusBadge" class="status-badge status-safe">17.0 ft • Safe</div>
  </div>

  <script>
    // Coordinate mapping & tidal math
    // y(t) = 9 + 8 * cos( pi / 6.21 * (t - 4) )
    // Safe threshold: y = 13 ft => t in [1.93, 6.07]
    const W = 560, H = 340;
    const padL = 48, padR = 24, padT = 44, padB = 40;
    const plotW = W - padL - padR;
    const plotH = H - padT - padB;

    const tMin = 0, tMax = 8;
    const yMin = 0, yMax = 20;

    function fx(t) { return padL + ((t - tMin) / (tMax - tMin)) * plotW; }
    function fy(y) { return padT + ((yMax - y) / (yMax - yMin)) * plotH; }
    function depth(t) { return 9 + 8 * Math.cos((Math.PI / 6.21) * (t - 4)); }

    // Render static grid & mathematically exact curves
    const gridLayer = document.getElementById('gridLayer');
    
    // Y-Grid
    for (let y = 0; y <= 20; y += 4) {
      const yPos = fy(y);
      const line = document.createElementNS('http://www.w3.org/2000/svg', 'line');
      line.setAttribute('x1', padL);
      line.setAttribute('x2', W - padR);
      line.setAttribute('y1', yPos);
      line.setAttribute('y2', yPos);
      line.setAttribute('class', y === 0 ? 'axis-line' : 'grid-line');
      gridLayer.appendChild(line);

      const txt = document.createElementNS('http://www.w3.org/2000/svg', 'text');
      txt.setAttribute('x', padL - 8);
      txt.setAttribute('y', yPos + 4);
      txt.setAttribute('text-anchor', 'end');
      txt.setAttribute('class', 'tick-text');
      txt.textContent = y + ' ft';
      gridLayer.appendChild(txt);
    }

    // X-Grid
    const timeLabels = ['12 AM', '1 AM', '2 AM', '3 AM', '4 AM', '5 AM', '6 AM', '7 AM', '8 AM'];
    for (let t = 0; t <= 8; t += 1) {
      const xPos = fx(t);
      const line = document.createElementNS('http://www.w3.org/2000/svg', 'line');
      line.setAttribute('x1', xPos);
      line.setAttribute('x2', xPos);
      line.setAttribute('y1', padT);
      line.setAttribute('y2', H - padB);
      line.setAttribute('class', 'grid-line');
      gridLayer.appendChild(line);

      const txt = document.createElementNS('http://www.w3.org/2000/svg', 'text');
      txt.setAttribute('x', xPos);
      txt.setAttribute('y', H - padB + 18);
      txt.setAttribute('text-anchor', 'middle');
      txt.setAttribute('class', 'tick-text');
      txt.textContent = timeLabels[t];
      gridLayer.appendChild(txt);
    }

    // Build Curve Path & Shaded Polygons
    let dCurve = '';
    const nSteps = 160;
    for (let i = 0; i <= nSteps; i++) {
      const t = tMin + (i / nSteps) * (tMax - tMin);
      const x = fx(t);
      const y = fy(depth(t));
      dCurve += (i === 0 ? 'M' : 'L') + ` ${x.toFixed(2)} ${y.toFixed(2)}`;
    }
    document.getElementById('curvePath').setAttribute('d', dCurve);

    // Hazard Area (entire region under y=13 down to datum)
    const y13Pos = fy(13);
    const y0Pos = fy(0);
    let dHazard = `M ${fx(0)} ${y13Pos} L ${fx(8)} ${y13Pos} L ${fx(8)} ${y0Pos} L ${fx(0)} ${y0Pos} Z`;
    document.getElementById('hazardArea').setAttribute('d', dHazard);

    // Safe Area (under curve between t=1.93 and t=6.07, down to y=13)
    const t1 = 1.93, t2 = 6.07;
    let dSafe = `M ${fx(t1)} ${y13Pos}`;
    const safeSteps = 60;
    for (let i = 0; i <= safeSteps; i++) {
      const t = t1 + (i / safeSteps) * (t2 - t1);
      dSafe += ` L ${fx(t).toFixed(2)} ${fy(depth(t)).toFixed(2)}`;
    }
    dSafe += ` L ${fx(t2)} ${y13Pos} Z`;
    document.getElementById('safeArea').setAttribute('d', dSafe);

    // Threshold Line
    const thresh = document.getElementById('threshLine');
    thresh.setAttribute('x1', padL);
    thresh.setAttribute('x2', W - padR);
    thresh.setAttribute('y1', y13Pos);
    thresh.setAttribute('y2', y13Pos);

    // Peak dot
    const peakDot = document.getElementById('peakDot');
    peakDot.setAttribute('cx', fx(4));
    peakDot.setAttribute('cy', fy(17));

    // Vertical guides at 1.93 and 6.07
    const vg1 = document.getElementById('vGuide1');
    vg1.setAttribute('x1', fx(t1)); vg1.setAttribute('x2', fx(t1));
    vg1.setAttribute('y1', y13Pos); vg1.setAttribute('y2', H - padB);

    const vg2 = document.getElementById('vGuide2');
    vg2.setAttribute('x1', fx(t2)); vg2.setAttribute('x2', fx(t2));
    vg2.setAttribute('y1', y13Pos); vg2.setAttribute('y2', H - padB);

    // Interval Arrows
    const arrY = 56;
    const aL = document.getElementById('arrLeft');
    aL.setAttribute('x1', fx(t1) + 4); aL.setAttribute('x2', fx(4) - 4);
    aL.setAttribute('y1', arrY); aL.setAttribute('y2', arrY);

    const aR = document.getElementById('arrRight');
    aR.setAttribute('x1', fx(4) + 4); aR.setAttribute('x2', fx(t2) - 4);
    aR.setAttribute('y1', arrY); aR.setAttribute('y2', arrY);

    const txtL = document.getElementById('txtLeft');
    txtL.setAttribute('x', (fx(t1) + fx(4)) / 2);
    txtL.setAttribute('y', arrY - 6);
    txtL.textContent = 'Δt = -2.07h (1:56 AM)';

    const txtR = document.getElementById('txtRight');
    txtR.setAttribute('x', (fx(4) + fx(t2)) / 2);
    txtR.setAttribute('y', arrY - 6);
    txtR.textContent = 'Δt = +2.07h (6:04 AM)';

    // Interactive slider logic
    const slider = document.getElementById('timeSlider');
    const trackLine = document.getElementById('trackLine');
    const trackDot = document.getElementById('trackDot');
    const trackLabel = document.getElementById('trackLabel');
    const statusBadge = document.getElementById('statusBadge');

    function updateTracker(t) {
      const d = depth(t);
      const px = fx(t);
      const py = fy(d);

      trackLine.setAttribute('x1', px);
      trackLine.setAttribute('x2', px);
      trackLine.setAttribute('y1', py);
      trackLine.setAttribute('y2', H - padB);

      trackDot.setAttribute('cx', px);
      trackDot.setAttribute('cy', py);

      trackLabel.setAttribute('x', px);
      trackLabel.setAttribute('y', py - 10);

      const isSafe = d >= 13;
      statusBadge.className = 'status-badge ' + (isSafe ? 'status-safe' : 'status-hazard');
      statusBadge.textContent = `${d.toFixed(1)} ft • ${isSafe ? 'Safe Depth' : 'Hazard (<13 ft)'}`;
    }

    slider.addEventListener('input', (e) => {
      updateTracker(parseFloat(e.target.value));
    });

    updateTracker(4);
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Tidal Sinusoid Model</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      width: 100%;
      background: #f8f9fa;
      color: #1e2945;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      padding: 12px;
      display: flex;
      flex-direction: column;
      gap: 10px;
    }

    /* Top Equation Bar */
    .eq-bar {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      font-size: 15px;
      font-weight: 700;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 6px 12px;
      flex-wrap: wrap;
    }

    .eq-tag {
      padding: 2px 6px;
      border-radius: 6px;
      font-weight: 700;
      transition: background 0.2s, color 0.2s;
    }
    .tag-a { color: #0284c7; background: #e0f2fe; }
    .tag-b { color: #d97706; background: #fef3c7; }
    .tag-c { color: #059669; background: #d1fae5; }
    .tag-d { color: #7c3aed; background: #ede9fe; }

    /* SVG Graph Container */
    .graph-container {
      width: 100%;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 4px;
      position: relative;
    }

    svg {
      width: 100%;
      height: auto;
      display: block;
    }

    /* Highlight transitions */
    .graph-elem {
      transition: opacity 0.25s ease, stroke-width 0.25s ease;
    }

    .dimmed {
      opacity: 0.18 !important;
    }

    .active-elem {
      opacity: 1 !important;
      filter: drop-shadow(0 2px 4px rgba(0,0,0,0.12));
    }

    /* Cards Grid */
    .cards-grid {
      display: grid;
      grid-template-columns: repeat(4, 1fr);
      gap: 8px;
    }

    @media (max-width: 520px) {
      .cards-grid {
        grid-template-columns: repeat(2, 1fr);
      }
      .eq-bar {
        font-size: 13px;
      }
    }

    .param-card {
      background: #ffffff;
      border: 2px solid transparent;
      border-radius: 10px;
      padding: 8px 10px;
      cursor: pointer;
      box-shadow: 0 1px 3px rgba(0,0,0,0.05);
      transition: border-color 0.2s, background-color 0.2s, box-shadow 0.2s;
      user-select: none;
    }

    .param-card.active {
      box-shadow: 0 3px 8px rgba(0,0,0,0.1);
    }

    .card-d { border-color: #ede9fe; }
    .card-d.active { border-color: #7c3aed; background: #faf5ff; }

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      color: #64748b;
      margin-top: 1px;
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  </style>
</head>
<body>

  
  <div class="eq-bar">
    <span>Depth:</span>
    <span>y =</span>
    <span class="eq-tag tag-a" id="tagA">A</span>
    <span>cos(</span>
    <span class="eq-tag tag-b" id="tagB">B</span>
    <span>(t −</span>
    <span class="eq-tag tag-c" id="tagC">C</span>
    <span>)) +</span>
    <span class="eq-tag tag-d" id="tagD">D</span>
  </div>

  
  <div class="graph-container">
    <svg viewBox="0 0 580 270" id="waveSvg" aria-label="Tidal sinusoid graph showing High Tide, Low Tide, Midline, Amplitude, Period, and Shift">
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      <text x="335" y="246" font-size="11" fill="#64748b" text-anchor="middle">Low</text>
      <text x="545" y="246" font-size="11" fill="#d97706" text-anchor="middle" font-weight="700">C + T</text>
      <text x="555" y="246" font-size="11" fill="#64748b" font-weight="600" text-anchor="end">Time (t) →</text>

      
      <path id="waterArea" fill="url(#waterGrad)" class="graph-elem"
        d="M 55,230 
           L 55,62.8
           C 78,41 101,36 125,36 
           C 177,36 230,130 282,192
           C 308,223 321,224 335,224 
           C 349,224 362,223 388,192 
           C 440,130 493,36 545,36 
           L 545,230 Z" />

      
      <path id="waveCurve" fill="none" stroke="#0284c7" stroke-width="3.2" stroke-linecap="round"
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      <g id="elemA" class="graph-elem">
        <line x1="125" y1="130" x2="195" y2="130" stroke="#94a3b8" stroke-width="1" stroke-dasharray="2,2" />
        <line x1="125" y1="36" x2="195" y2="36" stroke="#94a3b8" stroke-width="1" stroke-dasharray="2,2" />
        
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        <text x="242" y="87" fill="#0284c7" font-size="12" font-weight="700" text-anchor="middle">Amplitude (A)</text>
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      <g id="elemT" class="graph-elem">
        <line x1="125" y1="36" x2="125" y2="15" stroke="#d97706" stroke-width="1" stroke-dasharray="2,2" />
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      <text x="125" y="52" fill="#0284c7" font-size="11" font-weight="700" text-anchor="middle">High Tide</text>

      
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    </svg>
  </div>

  
  <div class="cards-grid">
    <div class="param-card card-d active" id="cardD" onclick="selectParam('D')">
      <div class="card-header">
        <span class="param-title">Midline (D)</span>
      </div>
      <div class="param-formula">D = (Max + Min) / 2</div>
      <div class="param-sub">Vertical center / Avg depth</div>
    </div>

    <div class="param-card card-a active" id="cardA" onclick="selectParam('A')">
      <div class="card-header">
        <span class="param-title">Amplitude (A)</span>
      </div>
      <div class="param-formula">A = (Max − Min) / 2</div>
      <div class="param-sub">Peak height from midline</div>
    </div>

    <div class="param-card card-t active" id="cardT" onclick="selectParam('T')">
      <div class="card-header">
        <span class="param-title">Period & B</span>
      </div>
      <div class="param-formula">B = 2π / T</div>
      <div class="param-sub">T = Time peak to peak</div>
    </div>

    <div class="param-card card-c active" id="cardC" onclick="selectParam('C')">
      <div class="card-header">
        <span class="param-title">Shift (C)</span>
      </div>
      <div class="param-formula">C = First Peak Time</div>
      <div class="param-sub">Horizontal peak offset</div>
    </div>
  </div>

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          if (tag) tag.style.opacity = '0.35';
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    }

    // Initialize all visible
    updateView();
  </script>
</body>
</html>

OGM.12.TRG.4

Aligned learning resources

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