Answer:
30,150, 210 ,330
Step-by-step explanation:
1/sin^2x = 4
Multiply each side by sin^2x
1 = 4 sin^2 x
Divide each side by 4
1/4 = sin^2 x
Take the square root of each side
sqrt(1/4) = sqrt(sin^2 x)
±sqrt(1/4) = sin x
±1/2 = sinx
Take the inverse sin of each side
arcsin (1/2) = arcsin (sin x) and arcsin(-1/2) = arcsin (sin x)
30 = x -30 = x
But this is not between 0 and 360,
so we add 360
-30+360 = 330
We also have to look at the other locations where sin x = 1/2
Taking the arcsin only gives values between -90 and 90
Since we are looking at the sin value, we take 180 - the value given
180 -30 = 150
180 --30
180+30 = 210
So our values are 30, 150,210,330
