1. Solving for Exact Trigonometric Values Using the Unit Circle
18 April 2011

2. Reference Angles
Reference angles make it easier to find exact values of trig functions in the unit circle
An angle’s distance from the x-axis

3. Reference Angles, cont. Always Coterminal Acute (less than )
Have one side on the x-axis

4. Solving for Reference Angles
Step 1: Calculate the coterminal angle if necessary (Remember, coterminal angles are positive and less than 2π.)
Step 2: Sketch either the given angle (if less than 2π) or the coterminal angle (if greater than 360° or 2π)
Step 3: Determine the angle’s distance from the x-axis
This is the reference angle!!!!

5. Example:

6. Example:

7. Example:

8. Your Turn:

9. Your Turn:

10. Your Turn:

11. Your Turn:

12. Your Turn:

13. Solving for Exact Trig Values
Step 1: Solve for the reference angle (Note the quadrant)
Step 2: Identify the correct special triangle
Step 3: Identify the correct coordinates of the angle (Make sure the signs match the quadrant!)
Step 5: sin t = y-coordinate; cos t = x-coordinate;
Step 6: Rationalize the denominator if necessary

14. Example:
Reference Angle:
Special Triangle:

15. Example:
Coordinates:
Tangent:
Sine:
Cosine:

16. Example:
Reference Angle:
Special Triangle:

17. Example:
Coordinates:
Tangent:
Sine:
Cosine:

18. Example:
Reference Angle:
Special Triangle:

19. Example:
Coordinates:
Tangent:
Sine:
Cosine: