# Hyperbolic Trigonometric Functions **Hyperbolic Functions** are similar to the basic trigonometric functions, however they are related to the *hyperbolic curve* as opposed to the *unit circle*. These functions are defined in terms of $e^x$ and $e^{-x}$. | Function | Formula | | ----------------------------- | ----------------------------------------------------------------- | | Hyperbolic Cosine ($cosh$) | $cosh(x)=\frac{e^x+e^{-x}}{2}$ | | Hyperbolic Sine ($sinh$) | $sinh(x)=\frac{e^x-e^{-x}}{2}$ | | Hyperbolic Tangent ($tanh$) | $tanh(x)=\frac{sinh(x)}{cosh(x)}=\frac{e^x-e^{-x}}{e^x+e^{-x}}$ | | Function | Formula | | ----------------------------- | ----------------------------------------------------------------- | | Hyperbolic Cosecant ($csch$) | $csch(x)=\frac{1}{sinh(x)}=\frac{2}{e^x-e^{-x}}$ | | Hyperbolic Secant ($sech$) | $sech(x)=\frac{1}{cosh(x)}=\frac{2}{e^x+e^{-x}}$ | | Hyperbolic Cotangent ($coth$) | $tanh(x)=\frac{cosh(x)}{sinh(x)}=\frac{e^x+e^{-x}}{e^x-e^{-x}}$ | ## Inverse Hyperbolic Functions This is a sentence[^todo] [^todo]: This is the exmpalnation of the footnote