Question

Question #e3529

Answer 1

`x = pm 2/3 k pi` for `k =0,1,2,cdots`

Explanation:

`sin(2x)=-sinx = sin(-x)` then

`2x=-xpm 2kpi` and

`x = pm 2/3 k pi` for `k =0,1,2,cdots`

Answer 2

`x = kpi`, and
`x +- (2pi)/3 + 2kpi`

Explanation:

sin x + 2sin 2x = 0
sin x + 2sin x.cos x = 0
sin x(1 + 2cos x) = 0
a. sin x = 0 --> unit circle gives 3 solutions -->
x = 0, `x= pi`, and `x = 2pi`
b. 1 + 2cos x = 0
`cos x = - 1/2`
Trig table of special arcs and unit circle give -->
`x = +- (2pi)/3`
General answers
`x = kpi`, and
`x = +- (2pi)/3 + 2kpi`