Question

I'm supposed to solve for all radian solutions, but I have no idea where to begin with this one. I'd really appreciate a push in the right direction.
sin(x) + 2sin(x)cos(x) = 0

Answer 1

sin(x) can be factored out

Answer 2

if you factor out sin(x), what do you get?

Answer 3

sin(x) * (1 + cos(x))

Answer 4

1+2cos(x)
@Laine

Answer 5

you forgot the 2

Answer 6

oops forgot the 2
:)

Answer 7

now thats equal to 0

that means

sin(x)=0 and 1+2cos(x)=0

Answer 8

solve for x

Answer 9

thanks

Answer 10

\(\sin x+2\sin x\cos x=0\\(\sin x)(1+2\cos x)=0\)so either \(\sin x=0\) or \(1+2\cos x=0\) for our equation to hold. Solve both (I solved in the interval \((0,2\pi)\)):$$\sin x=0\\x=\pi$$and$$1+2\cos x=0\\2\cos x=-1\\\cos x=-\frac12\\x\in\left\{\frac{2\pi}3,\frac{4\pi}3\right\}$$

Answer 11

oops, I meant \(x\in\{0,\pi\}\) for the solution of \(\sin x=0\).

Answer 12

Thank you very much.