PLEASE HELP WITH THIS PROBLEM

Question

sin x = -0.32 on [0,2π).

Answer 1

First you will look at where Sine is negative in the unit circle (or quadrants). It is negative in the 3rd and 4th quadrant (so from 180 degrees, or π to 360 degrees, or 2π on the unit circle).

-.32 can be converted to a fraction (if you want to) = -8/25

To isolate and solve for x, you would take the inverse Sine of both sides:

1. X = Sin^-1(-8/25)
2. X ≈ -18.66° ; ≈ 341.34° This is for the 4th Quadrant.
3. For the 3rd quadrant, you would add this value to 180° to get X ≈ 198.66°
4. So your full answer is:
5. X = 198.66°, 341.34°

Does this make sense to you?

Answer 2

reference angle is about 18.7 degrees, use a calculator with an inverse sine function

sinx = -0.32

x = -18.7 = 341.3 degrees or 180+18.7 = 198.7 degrees

sines are <0 only in quadrants III or IV.

x = 198.7 or 341.3 degrees