Long trig equation

Question

sin(thetha) -2sin(thetha)Cos(thetha) =0

 

There are 4 answers to this but I dont know why there are so many. I only found 2 . 

Answer 1

Assuming θ is in the interval [0, 360°)

 

sin(θ) - 2sin(θ)cos(θ) = 0

sin(θ)(1 - 2 cos(θ)) = 0

 

This means sin(θ) = 0 or 1 - 2cos(θ) = 0

 

sin(θ) = 0, then θ = 0° or θ = 180°

 

1 - 2cos(θ) = 0

cos(θ) = 1/2

 

Since cos(θ) > 0, then there are values for θ in Quadrant 1 and Quadrant 4

In Quadrant 1, θ = 60°

In Quadrant 4, θ = 300°

 

∴ There are 4 solutions {0, 60°, 180°,  300°}