1. Using Fundamental Identities
Section 5.1
Using Fundamental Identities

2. Objective By following instructions students will be able to:
Recognize and write fundamental trigonometric identities.
Use fundamental trigonometric identities to evaluate trigonometric functions, simplify trigonometric expressions and rewrite trigonometric expressions.

3. Fundamental Trigonometric Identities
Reciprocal Identities
Quotient Identities
Pythagorean Identities

4. Fundamental Trigonometric Identities
Cofunction Identities
Even/Odd Identities

5. Candy Crush
Look for clues and patterns (4 or 5 candies that are the same).
More than one way to complete the level
One objective: clear the jellies.

6. Candy Crush No more lives? Get frustrated. Wait Look online for help.
Ask friends for help.
attempt again.

7. Trigonometric Proofs Look for clues and patterns (trig identities).
More than one way to complete the problem.
One objective: LHS=RHS

8. Trigonometric Proofs No more lives? Get frustrated. Wait
Look online for help.
Ask friends for help.
attempt again.

9. Example 1: Using Identities to Evaluate a Function
Use the values and to find the values of all six trigonometric functions.

10. Example 2: Simplifying a Trigonometric Expression

11. Example 3: Verifying Trigonometric Identities
Determine which of the following appears to be an identity. a) b)

12. Example 4: Verifying Trigonometric Identity
Verify the identity

13. Example 5: Factoring Trigonometric Expressions
Factor each expression. a) b)

14. Example 6: Factoring a Trigonometric Expression

15. Example 7: Simplifying a Trigonometric Expression

16. Example 8: Rewrite a Trigonometric Expression
Rewrite so that it is not in fractional form.

17. Example 9: Trigonometric Substitution
Use the substitution to express as a trigonometric function of .

18. Revisit Objective Did we…
Recognize and write fundamental trigonometric identities?
Use fundamental trigonometric identities to evaluate trigonometric functions, simplify trigonometric expressions and rewrite trigonometric expressions?

19. Homework
Pg 382 # 1-81 EOO