This one is throwing me off, I don't get how to do a identity equaling to -.3

Cos2x=-.3

This is not an identity. It is an equation to solve.

cos 2x = -.3
cos 72.5° = 0.3
But, we have -.3, so 2x is in QII or QIII

2x = 107.5° or 255.5°
x = 53.75° or 127.75°
You can also add 180° to each of those, since cos(2x) has period of pi. That will produce all the angles in [0°,360°)