Solve for theta in the interval 0 to 180

Question

2 sin theta = sin 2 theta 

Answer 1

2 sin θ = sin 2θ

 

Remember the formula for the sine of a double angle and use that on the right side:

2 sin θ = 2 sin θ cos θ

sin θ = sin θ cos θ

 

Get all the expressions with the variable on one side:

0 = sin θ cos θ - sin θ

 

Factor

0 = sin θ (cos θ - 1)

 

For this to be true, either sin θ is 0, or cos θ - 1 is 0

 

sin θ is 0 at 0° and 180°

 

cos θ - 1 = 0

cos θ = 1

 

cos θ is 1 also at 0° and 180°

 

So the solution is θ = 0° or θ =180°