Reference Angles:

The reference angle of q is smallest angle j between the terminal side of q and the x-axis.

Now, let P be a point on the terminal side of the angle and drop a perpendicular from P to the x-axis. By doing this, a natural right triangle is formed.

j is the angle between the leg along the x-axis and the hypotenuse and is also the reference angle of q.

If P has coordinates (x,y) and then the right triangle has dimensions:

The trig. functions j can be compared to the trig. functions of q, which are:

If j is the reference angle of an angle q, then the value of a trig. function of q is agreeable with the value of the same trig. function of j, except possibly for the sign.