7-4 Reference Angles

Finding Reference Angles Using Sin and Cosine

In order to find a reference angle, it must be between 0 degrees and 90 degrees.
There are 3 steps used in finding a reference angle:

1) Locate the original quadrant then sketch.

2) Decide whether the angle is positive or negative using the Unit Circle.

3) Subtract either 360 degrees or 180 degrees until your absolute value is between 0 degrees or 90 degrees.

Example 1: Find a reference angle for sin 1000 degrees.

*Before I can find the quadrant, I must subtract: 1000-360(2)=280. Now I can state the quadrant.

1) It is in quadrant four because 280 is between 275 and 360.

2) It is negative because sin is negative if it's in the third or fourth quadrant.

3) 280-360=-80

-The absolute value of -80 is 80.

answer: -sin 80 degrees

Example 2: Find a reference angle for cos (-50 degrees).

1) It is in quadrant four because -53 falls between -90 and 0.

2) It is positive because cos is positve if it's in the first and fourth quadrant.

3) Since -53 is already between 0 and 90, all you do is find the absolute value.

answer: cos 53 degrees

----Jordan Duhon