Precalculus (6th Edition) Blitzer

The trigonometric functions of a reference angle will give the absolute value of the corresponding functions for the original angle. Depending on which quadrant the original angle was located, we can determine the signs of the function and combine with the values from the reference angle. For example, the reference angle of $\theta=150^\circ$ is $30^\circ$; we have $cos(30^\circ)=\frac{\sqrt 3}{2}$. Since the angle is in quadrant II and $cos\theta\lt0$, we have $cos 150^\circ=-\frac{\sqrt 3}{2}$.