Question

How do I find all the solutions on the interval [0, 2pi) for sin2x+sinx=0?

Answer 1

\[2\sin x\cos x + \sin x = 0 \implies \sin x(2\cos x + 1) = 0\]\[\implies \sin x = 0,\quad \cos x = \frac{-1}2\]

Answer 2

so how do I make it to where I can set this equation to 0?

Answer 3

Think about it a little bit.

Answer 4

I thought 2sin(theta)cos(theta)=sin(2 theta)

Answer 5

you thought right.

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

Answer 6

ohhh I see where youre going with this

Answer 7

thank you sir

Answer 8

you're welcome :-)