My Questions | bartleby The "hyperbolic trigonometric functions "are speeme comDmations of ex- ponential functions that appear in application frequently enough that they have their own names. For example, the "hyperbolic cosine function" is given by 6. e* +e=* cosh r the "hyperbolic sine function" is given by sinh z 2 and the "hyperbolic tangent function" is given by sinh a tanh r cosh r (a) Use the definitions above to show that d tanh 1

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
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Chapter6: Trigonometric Functions: Unit Circle Approach
Section6.CR: Chapter Review
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6.
The "hyperbolic trigonometric functions are specIe comDmations of ex-
ponential functions that appear in application frequently enough that they have their
own names. For example, the "hyperbolic cosine function" is given by
e* +e-*
cosh r
2
the "hyperbolic sine function" is given by
sinh a
2
and the "hyperbolic tangent function" is given by
sinh a
tanh r
cosh z
(a)
Use the definitions above to show that
d
1
tanhr
dr
cosh² r
(b)
water with depth d is given by
The velocity of a water wave with length L moving across a body of
gL
2nd
tanh
27
Transcribed Image Text:My Questions | | bartleby 6. The "hyperbolic trigonometric functions are specIe comDmations of ex- ponential functions that appear in application frequently enough that they have their own names. For example, the "hyperbolic cosine function" is given by e* +e-* cosh r 2 the "hyperbolic sine function" is given by sinh a 2 and the "hyperbolic tangent function" is given by sinh a tanh r cosh z (a) Use the definitions above to show that d 1 tanhr dr cosh² r (b) water with depth d is given by The velocity of a water wave with length L moving across a body of gL 2nd tanh 27
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