Stitz-Zeager_College_Algebra_e-book

# In the english system of units pounds lbs is a

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online