Question

Why is cos(150⁰) not the same as cos(30⁰)?

Is this because of the sign values of the cos. trig function that makes it negative in the 2nd quadrant?

Answer 1

Yeah, cos 150° is negative because it's in the 2nd quadrant, which has all negative x-values. (The third quadrant has all negative x-values as well)
Cos 30° is positive because the first quadrant(and 4th) have all positive x-values.