Returns the inverse tangent (also called arctangent)

tanֿ¹(*number*)

Press:

- [2nd]
- [tanֿ¹]

TI-83/84/+/SE

1 byte

tanֿ¹( returns the arctangent of its argument. It is the inverse of tan(, which means that tanֿ¹(n) produces an angle θ such that tan(θ)=n.

Like tan(, the result of tanֿ¹( depends on whether the calculator is in Radian or Degree mode. However, unlike tangent, the result is in degrees or radians, not the argument. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion of θ=tanֿ¹(n) from radians to degrees is θ*180/π and from degrees to radians is θ*π/180. The tanֿ¹( command also works on a list.

tanֿ¹( will always return a value between -π/2 and π/2 (or -90° and 90°).

In radians:

```
:tanֿ¹(1)
.7853981634
```

In degrees:

```
:tanֿ¹(1)
45
```

# Optimization

Expressions of the form tanֿ¹(*y**/x*) are usually better recast as R►Pθ(*x*,*y*); the latter will not fail even if *x* should happen to be equal to zero.

# Error Conditions

**ERR:DATA TYPE**is thrown if you input a complex value or a matrix.

# Related Commands

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