Takes the hyperbolic cosecant of a number.

csch(*value*)

**Menu Location**

- Press 2nd MATH to enter the MATH menu.
- Press C to enter the Hyperbolic submenu.
- Press 4 to select csch(.

This command requires a calculator with AMS version 2.07 or higher (it will also work on any TI-89 Titanium or Voyage 200 calculator)

1 byte

The `csch()` command returns the hyperbolic cosecant of a number. Along with 11 other trig and hyperbolic functions, it was added in AMS version 2.07; on earlier versions, `csch(x)` can be replaced by 1/`sinh(x)`.

As long as the calculator is in radian mode, `csch()` can be used with complex numbers according to the rule that csch(** i**x)=-csc(x)

*****and csc(

*i***x)=-csch(x)**

*i******. This rule only works in radian mode, and

*i*`csch()`of a complex number will return a domain error when working in degrees or gradians.

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

```
:csch(0)
undef
:expand(csch(x))
1/(e^x+1)+1/(e^x-1)
:comDenom(1/(e^x+1)+1/(e^x-1))
1/sinh(x)
```

If `csch()` is applied to a list, it will take the hyperbolic cosecant of every element in the list. However, it can't be applied to matrices the way `sinh()` can (this is probably an oversight; all the trig and hyperbolic functions that were present in all AMS versions work with matrices, but the ones added in version 2.07 do not).

# Formulas

The definition of hyperbolic cosecant is, by analogy with `csc()`, the reciprocal of `sinh()`:

# Error Conditions

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