Takes the tangent of a number (usually, an angle).

tan(*angle*)

**Menu Location**

Press the TAN button to enter tan(.

This command works on all calculators.

1 byte

The `tan()` command returns the tangent of an angle measure. Naturally, the result depends on the angle `mode` the calculator is in: `radian`, `degree`, or (in AMS version 3.10) `gradian`. You can also use one of the ` ^{r}`,

`°`,

`marks to specify an angle mode.`

^{G}For many common angles, `tan()` can compute an exact result. Other angles, the calculator will leave alone unless it's in approximate mode (or unless you make it approximate), and then it will give a decimal approximation. As long as the calculator is in `radian` mode, `tan()` can be used with complex numbers as well.

```
:tan(60°)
√3
:tan(x+π)
tan(x)
:tan(ix)
tanh(x)*i
```

If `tan()` is applied to a list, it will take the tangent of every element in the list.

# Advanced Uses

The `tan()` of a matrix is not (in general) the same as taking the tangent 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.

# Error Conditions

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

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

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