Stitz-Zeager_College_Algebra_e-book

A y tan x 3 period 1 6 b y 2 tan 1 12 3 7 12 x 5 6 y

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Unformatted text preview: an(θ) = 3 when θ = (f) sec(θ) = 1 when θ = 2kπ for any integer k π 5π (g) csc(θ) = 2 when θ = + 2kπ or θ = + 2kπ for any integer k . 6 6 π (h) cot(θ) = 0 when θ = + kπ for any integer k 2 3π (i) tan(θ) = −1 when θ = + kπ for any integer k 4 (j) sec(θ) = 0 never happens 1 (k) csc(θ) = − never happens 2 π 5. (a) cot(t) = 1 when t = + kπ for any integer k 4 π (b) tan(t) = 1 when t = + kπ for any integer k 4 2 5π 7π (c) sec(t) = − √ when t = + 2kπ or t = + 2kπ for any integer k 6 6 3 (d) csc(t) = 0 never happens √ 5π + kπ for any integer k (e) cot(t) = − 3 when t = 6 √ 5π 3 (f) tan(t) = − when t = + kπ for any integer k 3 6 2 π 11π (g) sec(t) = √ when t = + 2kπ or t = + 2kπ for any integer k 6 6 3 π 2 2π (h) csc(t) = √ when t = + 2kπ or t = + 2kπ for any integer k 3 3 3 √ π (i) cot(t) = 3 when t = + kπ for any integer k 6 6. The tree is about 47 feet tall. 7. The lights are about 75 feet apart. 8. (b) The fire is about 4581 feet from the base of the tower. 9. The boat has traveled about 244 feet. 10. (a) The tower is about 682 feet tall. (b) The guy wire hits the ground about 731 feet away from the base of the tower. 10.4 Trigonometric Identities 10.4 655 Trigonometric Identities In Section 10.3, we saw the utility of the Pythagorean Identities in Theorem 10.8 along with the Quotient and Reciprocal Identities in Theorem 10.6. Not only did these identities help us compute the values of...
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