Cumulative Review AN61 92. ° = − ° = − = − = − sin15 1 cos30 2 1 3 2 2 2 3 4 2 3 2 ; ( ) ° = ° − ° = ° ° − ° ° = ⋅ − ⋅ = − = − sin15 sin 45 30 sin45 cos30 cos45 sin30 2 2 3 2 2 2 1 2 6 4 2 4 6 2 4 ; ( ) ⎡ − ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ = − = − ⋅ = − = − + = ⎛ − ⎝ ⎜⎜⎜ ⎞ ⎠ ⎟⎟ ⎟ 2 3 2 2 3 4 4 2 3 4 4 8 4 3 16 6 2 12 2 16 6 2 4 2 2 93. θ θ ( ) = − cos 2 2 cos 1 2 Chapter Test (page 542) 1. π 6 2. π − 4 3. π − 3 4. π 2 5. π 4 6. π − 6 7. π 5 8. 7 3 9. 3 10. − 4 3 11. 0.39 12. 0.78 13. 1.25 14. 0.20 15. θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ ( )( ) ( )( ) + + = + + ⋅ − − = − + − = + − csc cot sec tan csc cot sec tan csc cot csc cot csc cot sec tan csc cot 1 sec tan csc cot 2 2 θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ ( ) ( )( ) ( ) = + − ⋅ − − = − − − = − − 1 sec tan csc cot sec tan sec tan sec tan sec tan csc cot sec tan csc cot 2 2 16. θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ + = ⋅ + = + = + = = sin tan cos sin sin cos cos sin cos cos cos sin cos cos 1 cos sec 2 2 2 2 17. θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ ( ) ( ) + = + = + = + = = = = tan cot sin cos cos sin sin sin cos cos sin cos sin cos sin cos 1 sin cos 2 2 sin cos 2 sin 2 2 csc 2 2 2 2 2 18. α β α β α β α β α α β β α β α β α β α β α β α β α β α β α β α β α β ( ) + + = + + = + + = + + sin tan tan sin cos cos sin sin cos sin cos sin cos cos sin sin cos cos cos cos sin cos cos sin cos cos sin sin cos cos sin cos cos α β α β α β α β α β α β = + ⋅ + = sin cos cos sin 1 cos cos sin cos cos sin cos cos 19. θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ ( ) ( ) ( ) ( ) ( ) = + = + = ⋅ − + ⋅ = − + sin 3 sin 2 sin cos2 cos sin2 sin cos sin cos 2 sin cos sin cos sin 2 sin cos 2 2 2 3 2 θ θ θ θ θ θ θ θ θ θ θ ( ) = − = − − = − − = − 3 sin cos sin 3 sin 1 sin sin 3 sin 3 sin sin 3 sin 4 sin 2 3 2 3 3 3 3 20. θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ θ ( ) − + = − + = − + = − + = − − = − tan cot tan cot sin cos cos sin sin cos cos sin sin cos sin cos sin cos sin cos sin cos sin cos 1 cos cos 1 1 2 cos 2 2 2 2 2 2 2 2 2 2 2 21. ( ) + 1 4 6 2 22. +2 3 23. 5 5 24. 12 85 49 25. ( ) − 2 13 5 3 39 26. +2 3 4 27. 6 2 28. 2 2 29. π π π π { } 3 , 2 3 , 4 3 , 5 3 30. π { } 0, 1.911, , 4.373 31. π π π π { } 3 8 , 7 8 , 11 8 , 15 8 32. { } 0.285, 3.427 33. { } 0.253, 2.889 Cumulative Review (page 543) 1. { } − − − + 1 13 6 , 1 13 6 2. ( ) + = − − y x 1 1 4 , or ( ) + = x y 3; 6 2; 1, 2 3. x-axis symmetry; ( ) ( ) ( ) − 0, 3, 0,3, 3,0 4. y 8 x 8 (6, 5) (3, 2) (0, 5) 5. y 5 x 6 (0, 1) y 5 22 6. y 0.5 x 2P 7. (a) y 2.5 x 2.5 (1, 1) (0, 0) (21, 21) y 5 x3 f 21(x) 5Ïx 3 (b) y 5 x 5 (0, 1) (1, e) f 21(x) 5 ln x 1 e 21, y 5 ex (c) y 1.25 x P (0, 0) f 21(x) 5 sin21 x P 2 , 2 21 P 2 , 1 y 5 sin x P 2 1, 2 P 2 21, (d) y 3 x P (0, 1) f 21(x) 5 cos21 x P 2 , 0 y 5 cos x (P, 21) (21, P) 8. (a) − 2 2 3 (b) 2 4 (c) 4 2 9 (d) 7 9 (e) +3 2 2 6 (f) − −3 2 2 6 9. 5 5 10. (a) − 2 2 3 (b) − 2 2 3 (c) 7 9 (d) 4 2 9 (e) 6 3 11. (a) ( ) ( )( ) ( ) = − − + f x x x x 2 1 1 1 ; 2 2 1 2 multiplicity 1; 1 and −1 multiplicity 2 (b) ( ) ( ) ( ) ( ) − − 0, 1; 1 2 ,0 ; 1,0 ; 1,0 (c) = y x2 5 (d) 2 22 22 2 (e) Local minimum value −1.33 at = − x 0.29, Local minimum value 0 at = x 1 Local maximum value 0 at = − x 1, Local maximum value 0.10 at = x 0.69 (f) y 1.25 x 1.25 (1, 0) (0, 21) (21, 0) 1 2 , 0 (0.69, 0.10) (20.29, 21.33) (g) Increasing: ( ] [ ] [ ) −∞− − ∞ , 1 , 0.29, 0.69, 1, Decreasing: [ ] [ ] − − 1, 0.29, 0.69,1 12. (a) { } − − 1, 1 2 (b) { } −1, 1 (c) ( ) ( ) −∞ − ∪ − ∞ , 1 1 2 , (d) ( ] [ ) −∞ − ∪ ∞ , 1 1,
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