Solve the trigonometric equation.

Question

Solve trigonometric equation on 0º≤x<360º and express answer in degrees to two decimal places.

15sin²(2x)+sin(2x)-2=0

Please and thank you!

Answer 1

15sin²(2x)+sin(2x)-2=0

let y=2x

15sin²y+siny-2=0

factor

(3siny-1)(5siny+2)=0

3siny-1=0

3siny=1

siny=1/3

siny=0.333...

use arcsin function

y=19.47122063º

y=2x

2x=19.47122063º

x=9.7356º

x=9.74º

5siny+2=0

5siny=-2

siny=-2/5=-0.4

use arcsin function

y=-23.578º

360-23.578º=336.422º

y=336.422º

y=2x

2x=336.42º

x=168.21º