1. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 Objectives: Use the formula for the cosine of the difference of two angles. Use sum and difference formulas for cosines and sines. Use sum and difference formulas for tangents. 5.2 Sum and Difference Formulas

2. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 2 The Cosine of the Difference of Two Angles

3. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 3 Example 1: Using the Difference Formula for Cosines to Find an Exact Value We know that Obtain this exact value using and the difference formula for cosines.

4. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 4 Example1 Continued Using the difference formula for Cosines

5. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 5 Example 2: Using the Difference Formula for Cosines to Find an Exact Value Find the exact value of

6. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 6 Example 3: Verifying an Identity Verify the identity:

7. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 7 Example 3: (continued) Continued The identity is verified.

8. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 8 Sum and Difference Formulas for Cosines and Sines

9. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 9 Example 4: Using the Sine of a Sum to Find an Exact Value Find the exact value of using the fact that

10. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 10 Example 4 Continued Use the sum of sines formula

11. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 11 Example 5 part A: Finding Exact Values Suppose that for a quadrant II angle and for a quadrant I angle Find the exact value of

12. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 12 Example 5 Part B Suppose that for a quadrant II angle and for a quadrant I angle Find the exact value of

13. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 13 Example 5 Part C Suppose that for a quadrant II angle and for a quadrant I angle Find the exact value of

14. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 14 Example 5: Part D Suppose that for a quadrant II angle and for a quadrant I angle Find the exact value of

15. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 15 Sum and Difference Formulas for Tangets

16. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 16 Example 6: Verifying an Identity Verify the identity:

17. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 17 Example 7 Find the exact value of = tan(20º + 100º) = tan 120º =

18. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 18 Example 8 If sin A = and A is in the third quadrant, cos B = and B is in the fourth quadrant, evaluate each of the following: A) sin(A − B) B) cos(A − B) C) tan(A − B)

19. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 19 Example 8 Continued sin(A − B) = cos(A − B) = tan(A − B) = 12 −3 5 −4 13 −5 sin A cos B − cos A sin B cos A cos B + sin A sin B