1. Chapter 4: Circular Functions Lesson 4: Trigonometric Identities Mrs. Parziale

2. Do Now Given the triangle below. How would you find the length of the missing side? 3 inches 4 inches ? inches

3. Trigonometric Identities Pythagorean Identity.

4. Example 1: If, then and. Show the Pythagorean identity holds:

5. Example 2: If, use the Pythagorean Identity to find.

6. Opposites Theorem: Compares  and -  Rotate in OPPOSITE (clockwise) direction

7. Properties of Supplements (For  measured in radians)

8. Properties of Complements: (For  measured in radians)

9. Example 3: Given:, without a calculator find and

10. Example 4: Find the following trig values: (hint: label a unit circle with appropriate coordinates at and use those coordinates):

11. Half-Turn Theorem: Think in terms of what we know about odd functions. If (x,y) is on the graph, so too is (-x, -y) because odd functions are rotations of 180 degrees

12. Example 5: Calculate the exact values of the following (use your unit table knowledge to help you.) a) Find the following when (First find cos, sin, and tan of each angle)

13. Example 6: Given,  is measured in radians and. Evaluate the following without a calculator. a)b)

14. Example 7: Given,, evaluate the following without a calculator. a) b)

15. Example 7, cont.: Given,, evaluate the following without a calculator. c) d)

16. Closure If, find. If, find and. Using the unit circle, explain why for all 