If 0º≤ x < 360º, what are the solutions of 3 sin x = 2 cos² x?

Question

a 30º, 150º

b 30º, 120º

c 30º, 330º

d 150º, 330º

Answer 1

do your homework yourself.

Answer 2

3 sin x = 2 cos² x

3 sin x = 2(1 - sin² x)

3 sin x = 2 - 2 sin² x

2 sin² x + 3 sin x - 2 = 0

This is a quadratic equation, which is factorized as,

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

(sin x + 2) =0 OR (2 sin x - 1) = 0

sin x = -2 OR sin x = 1/2

sin x -2 is impossible so sin x =1/2

x = 30º, 150º

Answer (a)

Answer 3

2 cos ² x - 3 sin x = 0

2 (1 - sin ² x) - 3 sin x = 0

2 sin ² x + 3 sin x - 2 = 0

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

sin x = 1 / 2

x = 30° , x = 150°

OPTION a