The cosh() Command

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Command Summary

Takes the hyperbolic cosine of a number.

Command Syntax

cosh(value)

Menu Location

• Press 2nd MATH to enter the MATH menu.
• Press C to enter the Hyperbolic submenu.
• Press 2 to select cosh(.

Calculator Compatibility

This command works on all calculators.

Token Size

1 byte

The cosh() command returns the hyperbolic cosine of a number.

As long as the calculator is in radian mode, cosh() can be used with complex numbers according to the rule that cosh(ix)=cos(x) and cos(ix)=cosh(x). This rule only works in radian mode, and cosh() of a complex number will return a domain error when working in degrees or gradians.

Occasionally, cosh() can compute an exact result; most of the time, the calculator will leave an expression with cosh() alone unless it's in approximate mode (or you force an approximation). When cosh() is used with symbolic expressions, the calculator can go back and forth between the cosh() expression and its exponential equivalent.

:cosh(0)
           1
:expand(cosh(x))
          e^x/2+1/(2*e^x)
:comDenom(e^x/2+1/(2*e^x))
          cosh(x)

If cosh() is applied to a list, it will take the hyperbolic cosine of every element in the list.

Advanced Uses

The cosh() of a matrix is not (in general) the same as taking the hyperbolic cosine of every element of the matrix. A different definition is used to compute the result; see Matrices and Their Commands. It requires the matrix to be square and diagonalizable in order to apply.

Formulas

The definition of hyperbolic cosine is given in terms of exponents:

(1)

\begin{align} \cosh{x} = \frac{e^x+e^{-x}}{2} \end{align}

Error Conditions

230 - Dimension happens when taking cosh() of a matrix that isn't square.

260 - Domain error happens when taking cosh() of a complex number in degree or gradian mode.

665 - Matrix not diagonalizable happens when taking cosh() of a matrix that isn't diagonalizable.

Related Commands

• sinh()
• tanh()
• coshֿ¹()