Section 7-5
1
Math 150 Lecture Notes
Trigonometric Equations
To solve a trigonometric equation:
1. Use rules of algebra to isolate the trig function on one side of the equal sign.
2. Use knowledge of the values of the trig functions to solve for the variable.
Example 1: Find all solutions of each equation.
sin x + 1 = 0 1 – tan
2
x = 0 cos 3x = sin 3x
tan
5
x = 9 tan x 4 sin x cos x + 2 sin x – 2 cos x = 1
Example 2: Find all solutions of each equation in the interval [0, 2π).
tan x = 3 cot x 2 sin
2
x = cos x + 1 3 csc
2
x = 4
