Question

what is the principal angle in the circle ?

Answer 1

Hmm, I'll give you can example b/c I can't put it into words.
Let's say we have the angle 150 degrees. Its principal angle is 30 degrees because it is 30 degrees away from the x axis (180 degrees - 150 degrees = 30). The properties of 150 are almost similar to those of 30.

Answer 2

Let's look at sin, cos, and tan of 30. In order, it'll be 1/2, sqrt(3)/2, and 1/sqrt(3). 150 degrees will have the same numbers BUT cos and tan will be negative.