Reference Angles

Reference Angles are like reduced fractions. They must be between 0degrees and 90degrees.

Steps:
1. Find the original quadrant and sketch.
2. Determine if the angle is positive or negative using unit circle methods.
3. Subtract 360degrees or 180degrees until theta is between 0degrees and 90degrees.

Example 1:
Express each of the following in terms of a reference angle.
a. sin128degrees
subtract 180
=52
sin 128 is positive in the second quadrant
=sin52degrees
b. cos128degrees
subtract 180
=52
cos128 is negative in the second quadrant
=-cos52degrees

Example 2:
Express each of the following in terms of a reference angle.
a. sin310degrees
subtract 360
=50
sin310 is negative in the fourth quadrant
=-sin50degrees
b. sin1000degrees
subtract 360
=640degrees
subtract 360
=sin280
subtract 180
=80
sin280degrees is negative in the fourth quadrant
=-sin80degrees

Example 3:
Express each of the following in terms of a reference angle.
a. cos224.5degrees
subtract 180
=44.5
cos 224.5 is negative in the third quadrant