Question

Find all solutions in the interval [0, 2π) sin2x + sin x = 0

Answer 1

Over the interval [0, 2π), what are the solutions to sin(2x) = sin(x)? Check all that apply.

0

StartFraction pi Over 3 EndFraction

StartFraction 2 pi Over 3 EndFraction

Pi

StartFraction 5 pi Over 3 EndFraction

Explanation:

Answer 2

sin 2 x + sin x = 0
( sin 2 x = 2 sin x cos x )
2 sin x cos x + sin x = 0
sin x ( 2 cos x + 1 ) = 0
sin x = 0
x 1 = 0
x 2 = π
or: 2 cos x + 1 = 0
2 cos x = - 1
cos x = -1/2
x 3 = 2π/3
x 4 = 4π/3