Need help with a trig problem please

Question

I can't figure out how to do this problem. It says

Solve the equation on the interval 0<=theta<2pi

Sin(2theta)=-1/2

I can't figure out what the solution set is. Im stuck. Can anyone help? Is there even a solution?

Answer 1

sin(2θ)=-1/2

sin is -1/2 at 210° and at 330° on the unit circle

so, 210/2=105° and 330/2=165°

θ=105° and 165°

also, sin has a period of 180°

105+180=285° and 165+180=345°

θ=285° and 345° also

there are four answers: 105°, 165°, 285° , and 345°

check: 2*285=570, 570-360=210°

2*345=690, 690-360=330°

Answer 2

sin 2θ = -0.5, 2θ is in QIII or QIV

2θ = 7π/6, 11π/6