(f) Using Euler’s formula, ejθ = cos θ+j sin θ, and the definitions of sech and coth in terms of the exponential function, derive the following relationships between the hyperbolic and trigonometric function. (ii) coth(x) = j cot(jx).

(f) Using Euler’s formula, ejθ = cos θ+j sin θ, and the definitions of sech and coth in terms of the exponential function, derive the following relationships between the hyperbolic and trigonometric function. (ii) coth(x) = j cot(jx).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section: Chapter Questions

Problem 81RE

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Question

(f) Using Euler’s formula, e^jθ = cos θ+j sin θ, and the definitions of sech and coth in terms of the exponential function, derive the following relationships between the hyperbolic and trigonometric function.

(ii) coth(x) = j cot(jx).

Expert Solution