Question

Let sin(2x) = cos(x), where 0° ≤ x < 180°. What are the possible values for x?

30° only
90° only
30° or 150°
30°, 90°, or 150°

Answer 1

D. 30°, 90°, or 150°

Explanation:

got it right on edge :)

Answer 2

Double angle identity for sine:

sin(2x) = 2 sin(x) cos(x)

So rewrite the equation as

sin(2x) = cos(x)

2 sin(x) cos(x) = cos(x)

2 sin(x) cos(x) - cos(x) = 0

cos(x) (2 sin(x) - 1) = 0

There are two cases,

cos(x) = 0 or 2 sin(x) - 1 = 0

cos(x) = 0 or sin(x) = 1/2

In the interval 0º ≤ x < 180º, we have cos(90º) = 0 and sin(30º) = sin(150º) = 1/2, so the possible values are 30º, 90º, or 150º.