Stitz-Zeager_College_Algebra_e-book

Since the wheel completes two revolutions in 2

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Unformatted text preview: ch simplifies the Trigonometry associated with the inverse functions, but complicates the Calculus; the other makes the Calculus easier, but the Trigonometry less so. We present both points of view. 10.6.1 Inverses of Secant and Cosecant: Trigonometry Friendly Approach In this subsection, we restrict the secant and cosecant functions to coincide with the restrictions on cosine and sine, respectively. For f (x) = sec(x), we restrict the domain to 0, π ∪ π , π 2 2 y y 1 π x π π 2 −1 π 2 reflect across y = x f (x) = sec(x) on 0, π 2 π ,π 2 ∪ −1 switch x and y coordinates f −1 (x) −− − − − −→ −−−−−− 1 x = arcsec(x) and we restrict g (x) = csc(x) to − π , 0 ∪ 0, π . 2 2 y y 1 π 2 −π 2 π 2 x −1 −1 reflect across y = x f (x) = csc(x) on 0, π 2 ∪ 0, π 2 −− − − − −→ −−−−−− switch x and y coordinates 1 x −π 2 f −1 (x) = arccsc(x) Note that for both arcsecant and arccosecant, the domain is (−∞, −1]...
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