sin(x/2) = -3/5, find all values of x that satisfies the equation. show your algebra.

Question

I don't understand this question:( my teacher gave us the answer, but I'm not sure how he got it. His answer was x/2 approximately ewqals 37 degrees for the reference angle. sine is negative in the 3rd and 4th quadrants, so x/2 approximately equals -37 degrees and -143 degrees. answer is -37degrees +360n and -143degrees +360n.

The formula needed is sin x/2= +- sqrt ((1-cosx)/2)

Answer 1

sin(x/2) =-3/5

x/2 = sin^-1(-3/5)

use a calculator with an inverse sine function to find the inverse sine of 3/5=the reference angle = about 36.87 degrees

x/2 = -37+360n or -143+360n degrees where n= any integer

x = -74+360n degrees or -286+360n=74+360n degrees where n= any integer

x = + 74 +360n degrees