Public learning track
Radian Measure, the Unit Circle, and Small-Angle Approximations
11th Grade · Math · Open Global Math
9 lessons
Goal
Master radian angle measure, arc length, sector area, exact trigonometric values, and small-angle approximations.
Featured Diagrams
Radian Measure as Arc Length on the Unit Circle
9 lessons
0 of 9 done
- 1Radian Measure as Arc Length on the Unit CircleUp nextStart
- 2Calculating Arc Length and Perimeter of Circular SectorsPremiumNot started yet
- 3Area of Circular Sectors and SegmentsNot started yet
- 4Exact Trigonometric Values on the Unit CircleNot started yet
- 5Exact Trigonometric Values for Quadrantal Angles and Multiples of πNot started yet
- 6Exact Values of Reciprocal Trig Functions for Special AnglesNot started yet
- 7Small-Angle Approximations for Sine and TangentNot started yet
- 8Small-Angle Approximation for CosineNot started yet
- 9Evaluating Limits and Expressions Using Small-Angle ApproximationsNot started yet
Standards Covered
- 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).
- 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.
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.