Reference Angles and the Rest of the Unit Circle
Reference Angles
For any terminal point on the unit circle, define the reference angle as the smallest angle from the axis. In. The reference angle is positive regardless of direction. It is used to compare angles to first quadrant angles to obtain the absolute values of the sine and cosine functions. Since the cosine and sine functions correspond to the x and y coordinates of the terminal point, the signs of the functions are determined by the table below. Rather than memorizing the chart, it is recommended to visualize the coordinates in the unit circle.
Examples are shown in the applet below. Predict the reference angle, , the quadrant, and the sine and cosine of any of the displayed angles. Then click on any of the points confirm your values.
| Quadrant of terminal point of | ||||
| + | + | |||
| - | + | |||
| - | - | |||
| + | - |
Below is a completed unit circle with the remaining familiar angles and their coordinates You should recreate this until you are familiar with it. It is also a good idea to include angles expressed in degrees.