Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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maths help can you do d) please

Consider the hyperbolic functions, and their inverses, as real functions of a real variable.
(a) Define the following hyperbolic functions directly in terms of the exponential function
(i) sinh.
(ii) cosh.
(iii) sech.
(b) Sketch, on separate graphs, each of the functions in part (a).
(c) Prove, using the definitions of sinh and cosh in terms of the exponential function, that
sinh(2x) = 2 sinh(x) cosh(x).
(d) Solve for x
17 cosh(x) — 13 sinh(x) = 13.
(Express your solution(s) in exact form.)
(e) If sech is restricted to the domain [0, ∞) it has a unique inverse, sech-¹. Using the
definition of sech in terms of the exponential function, derive the formula
(1+√1-x²)
sech ¹(x) = In
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Transcribed Image Text:Consider the hyperbolic functions, and their inverses, as real functions of a real variable. (a) Define the following hyperbolic functions directly in terms of the exponential function (i) sinh. (ii) cosh. (iii) sech. (b) Sketch, on separate graphs, each of the functions in part (a). (c) Prove, using the definitions of sinh and cosh in terms of the exponential function, that sinh(2x) = 2 sinh(x) cosh(x). (d) Solve for x 17 cosh(x) — 13 sinh(x) = 13. (Express your solution(s) in exact form.) (e) If sech is restricted to the domain [0, ∞) it has a unique inverse, sech-¹. Using the definition of sech in terms of the exponential function, derive the formula (1+√1-x²) sech ¹(x) = In
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