**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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