Where do sinh, cosh, and tanh come from? Watch

Physics4Life
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like how are they derived?
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Mr M
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(Original post by Physics4Life)
like how are they derived?
They are defined in terms of exponentials. They also have a geometric connection with the rectangular hyperbola. Google will answer this for you.
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Mr M
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(Original post by Physics4Life)
like how are they derived?
Here you go:

http://www.mathcentre.ac.uk/resource...cfunctions.pdf

http://lgsims96.hubpages.com/hub/Hyperbolic-Functions
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Physics4Life
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Thanks dude, really helpful
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ztibor
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(Original post by Physics4Life)
like how are they derived?
These came from the complex variable exponential function

\displaystyle e^{i\cdot x}=\cos x + i\cdot \sin x where i=\sqrt{-1}
so
\displaystyle e^{-i\cdot x}=\cos x - i\cdot \sin x

Adding them together and dividing by 2

\displaystyle \frac{e^{i\cdot x}+e^{-i\cdot x}}{2}=cosh (ix) =\cos x

and

\displaystyle \frac{e^{i\cdot x}-e^{-i\cdot x}}{2}=sinh (ix) =i\cdot \sin x

so with real variable

cosh (x)=\cos ix and sinh (x)=i\cdot \sin ix

that is these are trigonometric functions with complex variable
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