Takes the hyperbolic cosine of a number.

cosh(*value*)

**Menu Location**

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

This command works on all calculators.

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(** i**x)=cos(x) and cos(

**x)=cosh(x). This rule only works in radian mode, and**

*i*`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)# 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.