Stitz-Zeager_College_Algebra_e-book

From section 1021 2 4 we know t 127 t so we

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Unformatted text preview: ∪ [1, ∞). Taking a page from Section 2.2, we can rewrite this as {x : |x| ≥ 1}. This is often done in Calculus textbooks, so we include it here for completeness. Using these definitions, we get the following properties of the arcsecant and arccosecant functions. 10.6 The Inverse Trigonometric Functions 709 Theorem 10.28. Properties of the Arcsecant and Arccosecant Functionsa • Properties of F (x) = arcsec(x) – Domain: {x : |x| ≥ 1} = (−∞, −1] ∪ [1, ∞) – Range: 0, π ∪ 2 π 2,π – as x → −∞, arcsec(x) → π+ 2; as x → ∞, arcsec(x) → – arcsec(x) = t if and only if 0 ≤ t < – arcsec(x) = arccos 1 x π 2 or π 2 π− 2 < t ≤ π and sec(t) = x provided |x| ≥ 1 – sec (arcsec(x)) = x provided |x| ≥ 1 – arcsec(sec(x)) = x provided 0 ≤ x < π 2 or π 2 <x≤π • Properties of G(x) = arccsc(x) – Domain: {x : |x| ≥ 1} = (−∞, −1] ∪ [1, ∞) – Range: − π , 0 ∪ 0, π 2 2 – as x → −∞, arccsc(x) → 0− ; as x → ∞, arccsc(x) → 0+ – arccsc(x) = t...
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