Solving Trig Equations?

Question

Hokay, so basically I need to solve this problem on my homework and I got all the way to here:

Sin1/2(x) = -7/25

What do I do next?

you can't divide by sin1/2 because the x is actually the part of it.
I guess I should have put it like this:
sin(x/2) = -7/25

Answer 1

I'm not sure what resources you are allowed, but normally you would go to a table of sines and look up the angle whose sin is -0.28, which is the negative of the angle whose sin is 0.28.

In radians, the value is -0.2838, so x/2 = -0.2838 and x = -0.5676.

In degrees, the value is -16.26º, so x = -32.52º

Note that sin is a multi-valued function, and sin(π+ø) = -sinø

So an additional solution is x = 2*(π+0.2838) radian or x = 2*(108º+16.26º)

Answer 2

Divide -7/25 by the Sin of 1/2
and thats it kind of like basic algebra