Answered: (a) Define the following hyperbolic…

(a) Define the following hyperbolic functions directly in terms of the exponential function (i) sinh(x). (ii) cosh(x). (iii) tanh(x). (iv) cosech(x). (v) sech(x). (vi) coth(x).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 40RE

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Question

(a) Define the following hyperbolic functions directly in terms of the exponential function

(i) sinh(x).

(ii) cosh(x).

(iii) tanh(x).

(iv) cosech(x).

(v) sech(x).

(vi) coth(x).

(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
cosh(2x) = 1 + 2 sinh?(x).
%3D

(d) Derive the formula
cosh (x) = +In (x + /x² – 1)
±in (x + V* =
-

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