Public learning track
Periodic Modeling and Trigonometric Applications
11th Grade · Math · Open Global Math
6 lessons
Goal
Model real-world cyclical and oscillatory phenomena using sinusoidal functions and solve applied contextual problems using inverse trigonometric functions.
Featured Diagrams
Modeling Tidal and Water Depth Cycles with Sinusoids
6 lessons
0 of 6 done
- 1Modeling Tidal and Water Depth Cycles with SinusoidsUp nextStart
- 2Modeling Temperature and Seasonal Variation CyclesPremiumNot started yet
- 3Modeling Circular Motion and Ferris WheelsNot started yet
- 4Solving Real-World Periodic Timing Problems Using Inverse Trigonometric FunctionsNot started yet
- 5Harmonic Modeling of Wave Interference and SuperpositionNot started yet
- 6Trigonometric Modeling and Inverse Functions: Mixed PracticeNot started yet
Standards Covered
- OGM.12.TRG.2Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Graph and analyze periodic trigonometric functions and their reciprocals (sec, csc, cot) and inverses (arcsin, arccos, arctan), identifying amplitude, period, frequency, phase shift, midline, domain, and range.
- OGM.12.TRG.4Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Solve trigonometric equations algebraically and graphically over specified intervals, including quadratic forms in trigonometric ratios and multiple-angle equations, applying inverse functions in contextual modeling.
- OGM.12.TRG.3Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Prove and apply trigonometric identities including Pythagorean identities (sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = csc²θ), angle addition/subtraction, double-angle formulas, and express a cos θ + b sin θ in harmonic form R cos(θ ± α) or R sin(θ ± α).
- OGM.12.TRG.1Open Global Math Standards 2026™ · Math · Level 12 / High School 3 (Age 16) · Grade 11Define radian measure as arc length on the unit circle; compute arc length, sector area, and exact trigonometric values for standard angles (0, π/6, π/4, π/3, π/2 and integer multiples); apply small-angle approximations (sin θ ≈ θ, cos θ ≈ 1 - θ²/2, tan θ ≈ θ).
Curriculum Framework
11th Grade · Math · Open Global Math
1
9 lessons
Radian Measure, the Unit Circle, and Small-Angle Approximations
Master radian angle measure, arc length, sector area, exact trigonometric values, and small-angle approximations.
2
8 lessons
Graphs and Transformations of Trigonometric Functions
Analyze, graph, and interpret the primary and reciprocal trigonometric functions under vertical and horizontal transformations.
3
7 lessons
Inverse Trigonometric Functions and Graphs
Understand domain restrictions, graph inverse trigonometric functions, and evaluate compositions of trigonometric and inverse trigonometric functions.
4
8 lessons
Trigonometric Identities and Harmonic Forms
Prove and apply fundamental, Pythagorean, compound-angle, and double-angle identities, and convert linear combinations into harmonic form.
5
8 lessons
Solving Trigonometric Equations and Systems
Solve linear, quadratic, multiple-angle, and harmonic trigonometric equations both algebraically and graphically over defined domains.
6
6 lessons
Periodic Modeling and Trigonometric Applications
Model real-world cyclical and oscillatory phenomena using sinusoidal functions and solve applied contextual problems using inverse trigonometric functions.