1. Reference Angles

2. What is a Reference Angle? For any given angle, its reference angle is an acute version of that angle The values for the Trig. Functions of any angle are the SAME as the values of those functions for its reference angle (give or take a minus sign)

3. How to find a Reference Angle: For any angle in Standard Position, the reference angle is the smallest angle that can be created between the terminal side and the x-axis.

4. How to find a Reference Angle: 1.) You must begin with an angle between 0⁰ and 360⁰. - If the given angle is not between 0⁰ and 360⁰, then you must find a coterminal angle that is.

5. How to find a Reference Angle: 2.) Determine in which quadrant the terminal side for the angle is located. - 0⁰ to 90⁰: Quadrant 1 - 90⁰ to 180⁰: Quadrant 2 - 180⁰ to 270⁰: Quadrant 3 - 270⁰ to 360⁰: Quadrant 4

6. How to find a Reference Angle: 3.) Apply the proper formula to calculate the reference angle. - Quadrant 1: Do nothing - Quadrant 2: 180⁰ – θ - Quadrant 3: θ – 180⁰ - Quadrant 4: 360⁰ – θ

7. Example: θ = 495⁰

8. Practice 1: θ = – 275⁰

9. Practice 2: θ = 452⁰