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  • 1. 9-2: Addition and Subtraction Identities Learning Goals: Use the addition and subtraction identities for sine, cosine & tangent 2009 Roy L. Gover (www.mrgover.com)

2. Review Find the exact values: 1. sin 2. cos180 2 3. sin 4. sin 270 3 5. cos 6. cos 2 2 3. Review 60 30 1 23 45 45 1 1 2 4. Review 1 23 1 1 2 6 3 4 4 5. Review Find the exact values: 1. sin 30 2. tan 6 3. cos 45 4. sin 3 5 5. cos 6. tan220 4 6. Does cos 40+ cos 10=cos 50? Analysis Inquiring Minds Want To Know 7. cos(+)=cos cos-sin sin cos(-)=cos cos+sin sin Addition & Subtraction Identities for Cosine: Important Idea cos( ) cos cos sin sin = m 8. Example Find the exact value of cos 75 using the values of the function for 30 and 45 9. Example Find the exact value of cos using the values of the function for and 3 4 7 12 10. Try This Find the exact value of cos 15 using the values of the function for 60 and 45. Hint: cos 15=cos(60-45) 2 6 4 4 + 11. Try This Find exact value of cos using the values of the function for and . Hint: cos = cos 2 6 4 4 + 12 3 4 12 3 4 12. Example Rewrite the given expression in terms of sin x and/or cos x: cos(x + ) 13. sin(+)=sin cos+cos sin sin(-)=sin cos - cos sin Addition & Subtraction Identities for Sine: Important Idea sin( ) sin cos cos sin = 14. Example Find the exact value of sin 75. Simplify your answer. 15. Example Find exact value of sin Hint: Simplify your answer. 13 12 5 13 4 6 12 = 16. Try This Find exact value of sin Hint: 5 12 2 5 3 4 12 = Simplify your answer. 6 2 4 + 17. Try This Verify the identity: sin(270+x)=-cos x 18. Solution sin(270 ) sin 270 cos cos270 sin 1(cos ) 0(sin ) cos x x x x x x + = + = + = 19. tan tan tan( ) 1 tan tan + + = tan tan tan( ) 1 tan tan = + Addition & Subtraction Identities for Tangent Important Idea 20. tan tan tan( ) 1 tan tan = m Addition & Subtraction Identities for Tangent-the condensed form: Important Idea 21. Example Find the exact value of tan 15 using the values of the tan function for 45 and 30. Simplify your answer. 22. Try This If sin A= & cos B= , find tan(A+B). 4 5 3 5 24 7 23. Lesson Close Describe a method for finding the exact value of sin 105.