Reference Angles

First of all, you need to know that reference angles are like reduced fractions. They have to be between 0 degrees and 90 degrees.

Steps:

1. You have to find the quadrant and then sketch it.
2. Next, determine if it is a positive or negative angle by using the unite circle.
3. Then, subtract 360 degrees or 180 degrees from the original number until theta is between 0 degrees and 90 degrees.

Formulas you need to know:

• Sin(theta)=y/r
• Cos(theta)=x/r
• Tan(theta)=y/x
• Csc(theta)=r/y
• Sec(theta)=r/x
• Cot(theta)=x/y
  

Example 1: Find the reference angle for sin600

1. 600-360=240. 240 is in the third quadrant.
2. Sin=y/r=-1/1. So it is negative.
3. Now you have to subtract 240 from 180 which gives you 60.
4. Final answer: -sin60 degrees.

Example 2: Explain sin5Pi/4 as a reference angle.

1. First, you have to put the original problem in degrees. 5Pi/4 x 180/Pi=225 degrees.
2. 225 degrees is in the third quadrant. Sin=x/r=-1/1. So it is negative.
3. 225-180=45
4. Final answer: -sin45 degrees=-sinPi/4

Amber :)