540 CHAPTER 7 Analytic Trigonometry Sum-to-Product Formulas (p. 536) α β α β α β + = + − sin sin 2 sin 2 cos 2 α β α β α β − = − + sin sin 2 sin 2 cos 2 α β α β α β + = + − cos cos 2 cos 2 cos 2 α β α β α β − = − + − cos cos 2 sin 2 sin 2 Objectives Section You should be able to . . . Example(s) Review Exercises 7.1 1 Define the inverse sine function (p. 472) p. 473 1 2 Find the value of an inverse sine function (p. 474) 1–3 7, 10 3 Define the inverse cosine function (p. 475) p. 476 2 4 Find the value of an inverse cosine function (p. 476) 4, 5 8, 11 5 Define the inverse tangent function (p. 477) p. 478 3 6 Find the value of an inverse tangent function (p. 478) 6 9, 12 7 Use properties of inverse functions to find exact values of certain composite functions (p. 479) 7–9 15–23 8 Find the inverse function of a trigonometric function (p. 482) 10 30, 31 9 Solve equations involving inverse trigonometric functions (p. 482) 11 90, 91 7.2 1 Define the inverse secant, cosecant, and cotangent functions (p. 487) 4–6 2 Find the value of inverse secant, cosecant, and cotangent functions (p. 487) 1, 2 13, 14 3 Find the exact value of composite functions involving the inverse trigonometric functions (p. 489) 3–5 24–29 4 Write a trigonometric expression as an algebraic expression (p. 490) 6 32, 33 7.3 1 Solve equations involving a single trigonometric function (p. 493) 1–5 70–74 2 Solve trigonometric equations using a calculator (p. 496) 6 75 3 Solve trigonometric equations quadratic in form (p. 496) 7 78 4 Solve trigonometric equations using fundamental identities (p. 497) 8, 9 76, 77, 79 5 Solve trigonometric equations using a graphing utility (p. 498) 10 87–89 7.4 1 Use algebra to simplify trigonometric expressions (p. 504) 1 34–50 2 Establish identities (p. 505) 2–8 34–42 7.5 1 Use Sum and Difference Formulas to find exact values (p. 512) 1–5 51–56, 59–63(a)–(d), 92 2 Use Sum and Difference Formulas to establish identities (p. 516) 6–8 43, 44 3 Use Sum and Difference Formulas involving inverse trigonometric functions (p. 517) 9, 10 64–67 4 Solve trigonometric equations linear in sine and cosine (p. 518) 11, 12 81 7.6 1 Use Double-angle Formulas to find exact values (p. 525) 1 59–63(e), (f), 68, 69, 93 2 Use Double-angle Formulas to establish identities (p. 525) 2–5 46, 47, 80 3 Use Half-angle Formulas to find exact values (p. 528) 6, 7 57, 58, 59–63(g), (h), 92 7.7 1 Express products as sums (p. 535) 1 48 2 Express sums as products (p. 536) 2 49, 50 Review Exercises In Problems 1–6, state the domain and range of each function. 1. = − y x sin 1 2. = − y x cos 1 3. = − y x tan 1 4. = − y x sec 1 5. = − y x csc 1 6. = − y x cot 1 In Problems 7–14, find the exact value of each expression. Do not use a calculator. 7. − sin 11 8. − cos 01 9. − tan 11 10. ( ) − − sin 1 2 1 11. − ⎛ ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ − cos 3 2 1 12. ( ) − − tan 3 1 13. − sec 2 1 14. ( ) − − cot 1 1
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