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

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Hyperbolic Functions & Graphs
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Formula for sinh⁡x\sinh x

sinh⁡x=ex−e−x2\sinh x = \frac{e^x - e^{-x}}{2}

Formula for cosh⁡x\cosh x

cosh⁡x=ex+e−x2\cosh x = \frac{e^x + e^{-x}}{2}

Formula for tanh⁡x\tanh x

tanh⁡x=sinh⁡xcosh⁡x\tanh x = \frac{\sinh x}{\cosh x}

Range of cosh⁡x\cosh x

[1,∞)[1, \infty)

Range of tanh⁡x\tanh x

(−1,1)(-1, 1)

Symmetry type of sinh⁡x\sinh x

Odd function

Symmetry type of cosh⁡x\cosh x

Even function

Asymptotes of tanh⁡x\tanh x

y=−1y = -1 and y=1y = 1

What are hyperbolic functions defined using?

Exponential functions

Minimum value of cosh⁡x\cosh x

11

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