MATH 1330 Section 6.3

Solving Trigonometric Equations

Steps: Use basic algebra techniques to solve the equation of the trigonometric function [trig(x) = number] Determine the reference angle and quadrants. Use your knowledge of the unit circle to give answers. Adjust (if needed) for all solutions or for multiple angle questions.

Popper 26: Solve the following. Give all answers on [0,2π) 8 sin (x) = -4 a. π/6 and 7π/6 b. 5π/6 and 7π/6 c. 7π/6 and 11π/6 d. π/3 and 4π/3 2cos2(x) – cos(x) – 1 = 0 2π/3, 4π/3, and 0 b. π/3, 5π/3, and 0 c. 2π/3, 4π/3, and π d. π/3, 5π/3, and π 3 tan (2x) + 5 = 8 π/4, and 5π/4 b. π/8, and 5π/8 c. π/8, 5π/8, 9π/8, and 13π/8 d. 3π/8, 5π/8, 7π/8, and 11π/8

Popper 27: Give all answers between [0, 2π) 1. sin(x + (π/6)) = ½ a. 0 and 2π/3 b. 0 and 5π/6 c. π/6 and 5π/6 d. 0 and 11π/6 2. sec (2x) – 2 = 0 a. π/3, 5π/3 b. π/6, and 5π/6 c. π/6, 5π/6, 7π/6, and 11π/6 d. No Answer 3. tan(x) sin(x) = 0 a. 0, π/2, π, 3π/2 b. 0 and π c. 0 only d. 0, π/4, π, and 5π/4