Unit 7

Trigonometric Identities and Equations

Verify and apply fundamental, Pythagorean, sum/difference, double-angle, and half-angle identities. Solve trig equations.

Unit 7 · 8 pages

Lessons

Unit overview, essential questions, learning objectives, and vocabulary list for Unit 7 Trigonometric Identities & Equations.

Use Pythagorean, reciprocal, and quotient identities to simplify and solve trig equations.

Apply sin(A±B), cos(A±B), and tan(A±B) formulas to find exact values and simplify expressions.

Apply double-angle and half-angle formulas; use power-reduction identities to simplify expressions.

Convert sums of trig functions to products and products to sums for simplification and integration prep.

Solve trig equations on [0, 2π) and over all reals; use identities to reduce to single-function equations.

Build sinusoidal models from data; determine amplitude, period, phase shift, and vertical shift from context.

Consolidate your understanding of trig identities, sum/difference formulas, and solving trig equations.