Solving Trigonometric Equations T, 11.0: Students demonstrate an understanding of half-angle and double- angle formulas for sines and cosines and can use those formulas to prove and/or simplify other trigonometric identities.

Solving Trigonometric Equations Objectives Solve trigonometric equations on a restricted domain and justify each step Use the periodicity of the trigonometric functions to find the general solutions of a trigonometric equation. Key Words Quadrant Principle Values – Solutions are restricted to two adjacent quadrants

Pre-requisite Check Solve for xSolve for angle

Example 1

Example 2 Solve tan x sin 2 x + tan x cos 2 x = tan 2 x for 0 ≤  ≤ 2 .

Example 3

Example 4

Conclusions Summary Solve cos2x – cosx + 1 = 0 for 0≤x<360. – 60,90,270,300 Assignment Solving Trigonometric Equations – Page 459 – #(5-16)