Question

How do you solve `sin 2x + sin x = 0` over the interval 0 to 2pi?

Answer 1

`0, pi, (2pi)/3, (4pi)/3, 2pi`

Explanation:

sin 2x + sin x = 0
Apply the identity: sin 2x = 2sin x.cos x
2sin x.cos x + sin x = 0.
sin x(2cos x + 1) = 0
a. sin x = 0 --> `x = 0, x = pi and x = 2pi`
b/ 2cos x + 1 = 0
`cos x = -1/2` -->`x = +- (2pi)/3`
Answers for `(0, 2pi)`:
`0, pi, (2pi)/3, (4pi)/3, 2pi`
Reminder arc `(4pi)/3` is co-terminal to arc `-(2pi)/3`