Why are you doing anything with cosine or tangent?
What else is there to consider?
Say we have 3sinx = -3 from -pi to pi, for example.
x = sin^-1(-1)
So it's negative in the bottom quadrants.
If I go 90 from tan, it ends up at 270, and 90 from cos ends up at 360.
The book has the answer as -pi/2, or -90. Is this expressing it in its original form as a negative or what? I'm just really confused. I can do the positive domains fine.