Question

Select all that apply.

Solve for x , 0 < x < 360. 1/sin^2x = 4

answer choices (choose all that apply)
30
150
210
330

Answer 1

30,150, 210 ,330

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