Skip to main content
Engineering LibreTexts

6.3: Hyperbolic Functions

  • Page ID
    86647
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    Function Result

    acosh(x) 

    Inverse hyperbolic cosine; cosh –1 (x).

    acoth(x) 

    Inverse hyperbolic cotangent; coth –1 (x).

    acsch(x) 

    Inverse hyperbolic cosecant; csch –1 (x).

    asech(x) 

    Inverse hyperbolic secant; sech –1 (x).

    asinh(x) 

    Inverse hyperbolic sine; sinh –1 (x).

    atanh(x) 

    Inverse hyperbolic tangent; tanh –1 (x).

    cosh(x) 

    Hyperbolic cosine; cosh(x).

    coth(x) 

    Hyperbolic cotangent; cosh(x)/sinh(x).

    csch(x) 

    Hyperbolic cosecant; 1/sinh(x).

    sech(x) 

    Hyperbolic secant; 1/cosh(x).

    sinh(x) 

    Hyperbolic sine; sinh(x).

    tanh(x) 

    Hyperbolic tangent; sinh(x)/cosh(x).


    6.3: Hyperbolic Functions is shared under a CC BY 1.3 license and was authored, remixed, and/or curated by Brian Vick, Virginia Tech.

    • Was this article helpful?