1. Welcome to Precalculus!
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Write “I Can” statements.
I can:
Use sum and difference formulas to evaluate trigonometric functions, verify identities, and solve trigonometric equations.

2. Review
Attendance Questions from yesterday’s work

3. Sum and Difference Formulas 5.4
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4. Objective
Use sum and difference formulas to evaluate trigonometric functions, verify identities, and solve trigonometric equations.

5. Using Sum and Difference Formulas

6. Using Sum and Difference Formulas
In this section, you will study the uses of several trigonometric identities and formulas. Example 1 shows how sum and difference formulas can enable you to find exact values of trigonometric functions involving sums or differences of special angles.

7. Example 1 – Evaluating a Trigonometric Function
Find the exact value of . Solution: To find the exact value of , use the fact that Consequently, the formula for sin(u – v) yields

8. Example 1 – Solution
cont’d
Try checking this result on your calculator. You will find that 

9. Checkpoint 2

10. Checkpoint 3

11. Checkpoint 4

12. Example 5 – Proving a Cofunction identity
Use a difference formula to prove the cofunction identity Solution: Using the formula for cos(u – v), you have
= sin x.

13. Using Sum and Difference Formulas
Sum and difference formulas can be used to rewrite expressions such as and , where n is an integer as expressions involving only sin  or cos  . The resulting formulas are called reduction formulas.

14. Checkpoint 6

15. Example 8
The next example is a very important application from calculus. This technique is used to calculate several derivatives of trigonometric functions.

16. Example 8

17. Homework
Section 5.4 (Page 379) Problems 1 – 6 (Vocabulary), 8, 12, 36, 42, 48, 54, 57, 65, 80. Bonus: Problem 79 (5 points of extra credit on next quiz) Due Thursday