1. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 Objectives: Use the double-angle formulas. Use the power-reducing formulas. Use the half-angle formulas. Section 5.3 Double-Angle, Power-Reducing, and Half-Angle Formulas

2. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 2 Double-Angle Formulas

3. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 3 Example1 Part A: Using Double-Angle Formulas to Find Exact Values If and lies in quadrant II, find the exact value of

4. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 4 Example 1A Continued If and lies in quadrant II, find the exact value of

5. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 5 Example1 Part B If and lies in quadrant II, find the exact value of

6. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 6 Example1B Continued If and lies in quadrant II, find the exact value of

7. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 7 Example1 Part C: Using Double-Angle Formulas to Find Exact Values If and lies in quadrant II, find the exact value of

8. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 8 Example 1 C Continued If and lies in quadrant II, find the exact value of

9. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 9 Example 1 C Continued Continued

10. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 10 Example 2 Find the exact value of the trigonometric expression

11. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 11 Three Forms of the Double-Angle Formula for

12. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 12 Example3: Verifying an Identity Verify the identity: now expand using sin(A+B)

13. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 13 Example 3 Continued Cont. distribute Combine like terms

14. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 14 Half-Angle Formulas

15. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 15 Example 4: Using the Half-Angle Formula to Find an Exact Value Use to find the exact value of cos105°.

16. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 16 Example 4 Continued Use to find the exact value of cos105°.

17. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 17 Example 5 Find sin α/2, cos α/2, and tan α/2 if sec α = -5/4 and α lies in Quadrant II.

18. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 18 Half-Angle Formulas for Tangent

19. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 19 Power-Reducing Formulas - Look at but won’t assign

20. Copyright © 2014, 2010, 2007 Pearson Education, Inc. 20 Example: Reducing the Power of a Trigonometric Function Write an equivalent expression for sin 4 x that does not contain powers of trigonometric functions greater than 1.