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Math Help - csch(x) and tanh(x)...does the "h" mean anything?

  1. #1
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    csch(x) and tanh(x)...does the "h" mean anything?

    My teacher gave us a worksheet and sometimes I see csch(...) and tanh(...) and other times without the "h"

    Does the h mean anything or is this probably a typo?
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  2. #2
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    They're the Hyperbolic Functions, we define as follows

    \sinh=\frac{e^x-e^{-x}}2 and \cosh=\frac{e^x+e^{-x}}2
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  3. #3
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    Quote Originally Posted by Krizalid View Post
    They're the Hyperbolic Functions, we define as follows

    \sinh=\frac{e^x-e^{-x}}2 and \cosh=\frac{e^x+e^{-x}}2
    based on that...

    is tanh =

    \frac{e^x-e^{-x}}{e^x+e^{-x}} ?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by circuscircus View Post
    based on that...

    is tanh =

    \frac{e^x-e^{-x}}{e^x+e^{-x}} ?
    yes, \tanh x = \frac {e^x - e^{-x}}{e^x + e^{-x}} but it is usually just defined as \frac {\sinh x}{\cosh x}
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  5. #5
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    Quote Originally Posted by Jhevon View Post
    yes, \tanh x = \frac {e^x - e^{-x}}{e^x + e^{-x}} but it is usually just defined as \frac {\sinh x}{\cosh x}
    how do you integrate these functions? sinh, cosh and tanh?
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  6. #6
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    Quote Originally Posted by circuscircus View Post
    how do you integrate these functions? sinh, cosh and tanh?
    \int \sinh x dx = \cosh x + C

    \int \cosh x dx = \sinh x +C

    \int \tanh x dx = \int \frac{e^x - e^{-x}}{e^x + e^{-x}} dx let u=e^{x}+e^{-x}. Continue.
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  7. #7
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    Quote Originally Posted by circuscircus View Post
    how do you integrate these functions? sinh, cosh and tanh?
    \begin{aligned}\int\sinh\,dx&=\int\frac{e^x-e^{-x}}2\,dx\\&=\frac12(e^x+e^{-x})+k&\\&=\cosh+\,k,\,k\in\mathbb R\end{aligned}

    The same for \cosh
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