csc theata - 3 + 2sin theata = 0

Question

 precal I need help........ 

Answer 1

let θ=x

cscx-3+2sinx=0

cscx=1/sinx

1/sinx - 3 + 2sinx=0

multiply both sides by sinx

1-3sinx+2sin^2x=0

2sin^2x-3sinx+1=0

factor

(2sinx-1)((sinx-1)=0

set each factor to 0

2sinx-1=0

2sinx=1

sinx=1/2

sin is 1/2 at 30º and 180-30=150º

sinx-1=0

sinx=1

sin is 1 at 90º

answers are 30º, 90º, and 150º (+2∏k for k=0,±1,±2,±3,...)