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