Stitz-Zeager_College_Algebra_e-book

When constructing a table of values for the tangent

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Unformatted text preview: re the outputs from the inputs, which we have been calling t. 8 648 Foundations of Trigonometry Theorem 10.11. Domains and Ranges of the Circular Functions • The function f (t) = cos(t) • The function g (t) = sin(t) – has domain (−∞, ∞) – has domain (−∞, ∞) – has range [−1, 1] – has range [−1, 1] • The function F (t) = sec(t) = – has domain {t : t = π 2 1 cos(t) ∞ + πk, for integers k } = k=−∞ (2k + 1)π (2k + 3)π , 2 2 – has range {u : |u| ≥ 1} = (∞, −1] ∪ [1, ∞) • The function G(t) = csc(t) = 1 sin(t) ∞ – has domain {t : t = πk, for integers k } = (kπ, (k + 1)π ) k=−∞ – has range {u : |u| ≥ 1} = (∞, −1] ∪ [1, ∞) • The function J (t) = tan(t) = – has domain {t : t = π 2 sin(t) cos(t) ∞ + πk, for integers k } = k=−∞ (2k + 1)π (2k + 3)π , 2 2 – has range (−∞, ∞) • The function K (t) = cot(t) = cos(t) sin(t) ∞ – has domain {t : t = πk, for integers k } = (kπ, (k + 1)π ) k=−∞ – has range (−∞, ∞) The discussion on page 629 in Section 10.2.1 concerning solv...
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