solve sin2 theta = cos theta. the interval [0 degrees, 360 degrees]

Question

I am having trouble with knowing where to start this problem and my professor is online professor so I can't ask the questions without being through email and it is hard to communicate.

Answer 1

sin2θ=cosθ

sin2θ=2sinθcosθ

2sinθcosθ=cosθ

2sinθcosθ-cosθ=0

factor

cosθ(2sinθ-1)=0

cosθ=0 or 2sinθ-1=0

cosθ=0 when θ=90º or θ=270º (look on the unit circle)

2sinθ-1=0

2sinθ=1

sinθ=1/2

look on the unit circle and see that sinθ=1/2 when θ=30º

sin is positive in Quadrant2 as well as Quadrant 1

180º-30º=150º

θ=150º

answers:θ=90º, 270º, 30º, and 150º