Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: (b) tan2 (x) ≥ 1 (d) cos(2x) ≤ sin(x) 6. Solve each of the following equations, giving only the solutions which lie in [0, 2π ). Express the exact solutions using inverse trigonometric functions and then use your calculator to approximate the solutions to four decimal places. (a) sin(x) = 0.3502 (e) tan(x) = 117 (b) sin(x) = −0.721 (f) tan(x) = −0.6109 (c) cos(x) = 0.9824 (g) tan (x) = cos (x) (d) cos(x) = −0.5637 (h) tan (x) = sec (x) 7. Express the domain of each function using the extended interval notation. (See page 647 in Section 10.3.1 for details.) (a) f (x) = 1 cos(x) − 1 cos(x) (b) f (x) = sin(x) + 1 (c) f (x) = tan2 (x) − 1 (d) f (x) = 2 − sec(x) (e) f (x) = csc(2x) sin(x) (f) f (x) = 2 + cos(x) (g) f (x) = 3 csc(x) + 4 sec(x) 1 8. With the help of your classmates, determine the number of solutions to sin(x) = 2 in [0, 2π ). Then ﬁnd the number of solutions to sin(2x) = 1 , sin(3x) = 1 and sin(4x) = 1 in [0, 2π ). 2 2 2 A pattern should emerge. Explain how this pattern would help you solve equat...
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