Public learning track
Trigonometric Identities and Harmonic Forms
11th Grade · Math · Open Global Math
8 lessons
Goal
Prove and apply fundamental, Pythagorean, compound-angle, and double-angle identities, and convert linear combinations into harmonic form.
Featured Diagrams
Proving Pythagorean and Reciprocal Identities
8 lessons
0 of 8 done
- 1Proving Pythagorean and Reciprocal IdentitiesUp nextStart
- 2Simplifying Trigonometric Expressions Using Pythagorean IdentitiesPremiumNot started yet
- 3Sum and Difference Identities for Sine and CosineNot started yet
- 4Sum and Difference Identities for TangentNot started yet
- 5Deriving Double Angle Formulas from Addition FormulasNot started yet
- 6Proving Identities Using Addition and Double Angle FormulasNot started yet
- 7Expressing a cos θ + b sin θ in Harmonic Form R cos(θ ± α)Not started yet
- 8Expressing a cos θ + b sin θ in Harmonic Form R sin(θ ± α)Not started yet
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.