Hyperbolic Functions & Graphs (Edexcel A-Level Further Mathematics): Flashcards

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Hyperbolic Functions & Graphs
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Formula for sinhx\sinh x

sinhx=exex2\sinh x = \frac{e^x - e^{-x}}{2}

Formula for coshx\cosh x

coshx=ex+ex2\cosh x = \frac{e^x + e^{-x}}{2}

Formula for tanhx\tanh x

tanhx=sinhxcoshx\tanh x = \frac{\sinh x}{\cosh x}

Range of coshx\cosh x

[1,)[1, \infty)

Range of tanhx\tanh x

(1,1)(-1, 1)

Symmetry type of sinhx\sinh x

Odd function

Symmetry type of coshx\cosh x

Even function

Asymptotes of tanhx\tanh x

y=1y = -1 and y=1y = 1

What are hyperbolic functions defined using?

Exponential functions

Minimum value of coshx\cosh x

11

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