Trigonometric Equations

Michigan State University - Diagnostic Exam

Find the solution(s) to the equation $sinx tan x = sin x$ for $0≤ x < 2π$ .

a) $π -- 4$ b) $π 5π --, --- 4 4$ c) $π 0, -- 4$

d) $π 0, -, π 4$ e) $π 5π 0, -, π, --- 4 4$

Solution:

⇒ sin x tanx - sin x = 0 ⇒ sin x(tanx - 1 ) = 0 ⇒ sin x = 0 or tan x = 1

It follows that

sin x = 0 ⇒ x = 0, π π- 5-π tan x = 1 ⇒ x = 4 , 4

Diagnostic:

If you miss this question please review trigonometric equations.

July 15, 2008