Stitz-Zeager_College_Algebra_e-book

In the english system of units pounds lbs is a

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Unformatted text preview: coordinates −1 1 x f −1 (x) = arcsec(x) π and we restrict g (x) = csc(x) to 0, π ∪ π , 32 . 2 y y 3π 2 1 π π 2 π 3π 2 x −1 π 2 reflect across y = x g (x) = csc(x) on 0, π 2 ∪ π, 3π 2 −− − − − −→ −−−−−− switch x and y coordinates Using these definitions, we get the following result. −1 1 g −1 (x) = arccsc(x) x 712 Foundations of Trigonometry Theorem 10.29. Properties of the Arcsecant and Arccosecant Functionsa • Properties of F (x) = arcsec(x) – Domain: {x : |x| ≥ 1} = (−∞, −1] ∪ [1, ∞) π – Range: 0, π ∪ π , 32 2 – as x → −∞, arcsec(x) → 3π − 2; as x → ∞, arcsec(x) → – arcsec(x) = t if and only if 0 ≤ t < – arcsec(x) = arccos 1 x π 2 or π ≤ t < 3π 2 π− 2 and sec(t) = x for x ≥ 1 onlyb – sec (arcsec(x)) = x provided |x| ≥ 1 – arcsec(sec(x)) = x provided 0 ≤ x < π 2 or π ≤ x < 3π 2 • Properties of G(x) = arccsc(x) – Domain: {x : |x| ≥ 1} = (−∞, −1] ∪ [1, ∞) π – Range: 0, π ∪ π , 32 2 – as x → −∞, arccs...
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