Stitz-Zeager_College_Algebra_e-book

By denition then arccot2 radians which we can rewrite

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Unformatted text preview: ndations of Trigonometry 21. Write sin(3θ) and sin(5θ) as polynomials of sine. Can the same be done for sin(4θ)? If not, what goes wrong? 22. Write sin4 (θ) and cos4 (θ) as sums and/or differences of sines and/or cosines to the first power. 23. Verify the Product to Sum Identities. 24. Verify the Sum to Product Identities. 25. Write the following products as sums. (a) cos(3θ) cos(5θ) (b) sin(2θ) sin(7θ) (c) sin(9θ) cos(θ) 26. Write the following sums as products. (You may need to use a Cofunction or Even / Odd identity as well.) (a) cos(3θ) + cos(5θ) (c) cos(5θ) − cos(6θ) (e) sin(θ) + cos(θ) (b) sin(2θ) − sin(7θ) (d) sin(9θ) − sin(−θ) (f) cos(θ) − sin(θ) 10.4 Trigonometric Identities 10.4.2 Answers √ √ √ 2− 6 5. (a) 4 √ (b) 2 + 3 11. 1 − 671 √ 6− 2 (c) 4√ (d) −(2 + 3) x2 2 12. √ 14. (a) 2+ 2 15. (a) 14x + 49 (b) θ 2 • cos(2θ) = − • cos • cos 120 169 • cos = θ 2 θ 2 49 50 =− (b) 26. (a) 2 cos(4θ) cos(θ) 5 θ 2 √ 2− 2 √ 2+ 2 • tan...
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