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}, °, ^{G} marks to specify an angle mode.

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.