Trigonometric Equations

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 Helper

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 $cos(\theta)= 1[/math]. What values of [itex]\theta$ give that?

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

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.