How do I solve for the solutions of sin 2θ = sin θ in degrees?

[patriots1049]

Homework Statement

sin 2θ = sin θ Find the solutions in degrees.

Homework Equations

sin 2θ = 2sinθcosθ

The Attempt at a Solution

sin 2θ = sin θ
2sinθcosθ = sin θ
sinθ *cosθ/sin θ = 1

That's as far as I can get, and I think that is wrong. How do I procede from 2sinθcosθ = sin θ?

 

[HallsofIvy]

Homework Statement

sin 2θ = sin θ Find the solutions in degrees.

Homework Equations

sin 2θ = 2sinθcosθ

The Attempt at a Solution

sin 2θ = sin θ
2sinθcosθ = sin θ

One obvious possibility is $sin(\theta)= 0$. What values of $\theta$ give that?
IF $sin(\theta)\ne 0$, you can divide by it.

sinθ *cosθ/sin θ = 1

So cancel the $sin(\theta)$s, giving [itex]cos(\theta)= 1[/math]. What values of $\theta$ give that?<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> That's as far as I can get, and I think that is wrong. How do I procede from 2sinθcosθ = sin θ? </div> </div> </blockquote>[/itex]

 

[patriots1049]

Therefore the answer would be 0 degrees and 180 degrees? The book states that answers must greater or equal to one and less than 360.