Solving trig equation when sin is squared?

Question

2sin² (thetha) = 1 

 

When I solved , I got 2 of the answers right. But there are 4 answers. I got 45 and 135 degrees but the other two I have no idea how to find it. The other two answers are 225,315 degrees. 

Answer 1

2sin²(θ) = 1

 

sin²(θ) = 1/2

 

sin(θ) = ± √(2)/2

 

For sin(θ) = √(2)/2, since sin(θ) > 0 there are solutions in Quadrant 1 and Quadrant 2

In Quadrant 1, θ = 45°

In Quadrant 2, θ = 135°

 

For sin(θ) = -√(2)/2, since sin(θ) < 0 there are solutions in Quadrant 3 and Quadrant 4
In Quadrant 3, θ = 225°
In Quadrant 4, θ = 315°

 

There are four values for θ = {45°, 135°, 225°, 315°}

 

Answer 2

2sin² θ = 1

2sin² θ - 1 = 0

(√2 sin θ + 1)(√2√ sin θ - 1) = 0

 

Can you take it from here?