Arctan(x), tan-1(x), inverse tangent function.
Arctan definition
The arctangent of x is defined as the inverse tangent function of x when x is real (x∈ℝ).
When the tangent of y is equal to x:
tan y = x
Then the arctangent of x is equal to the inverse tangent function of x, which is equal to y:
arctan x= tan-1 x = y
Example
arctan 1 = tan-1 1 = π/4 rad = 45°
Graph of arctan
Arctan rules
| Rule name | Rule |
|---|---|
| Tangent of arctangent | tan( arctan x ) = x |
| Arctan of negative argument | arctan(-x) = - arctan x |
| Arctan sum | arctan α + arctan β = arctan [( |
α+β) / (1-αβ)] |
| Arctan difference | arctan α - arctan β = arctan [( α-β) / (1+αβ)] | | Sine of arctangent | | | Cosine of arctangent | | | Reciprocal argument | | | Arctan from arcsin | | | Derivative of arctan | | | Indefinite integral of arctan | |
Arctan table
| x | arctan(x) (rad) | arctan(x) (°) |
| --- | --- | --- | | -∞ | -π/2 | -90° | | -3 | -1.2490 | -71.565° | | -2 | -1.1071 | -63.435° | | -√3 | -π/3 | -60° | | -1 | -π/4 | -45° | | -1/√3 | -π/6 | -30° | | -0.5 | -0.4636 | -26.565° | | 0 | 0 | 0° | | 0.5 | 0.4636 | 26.565° | | 1/√3 | π/6 | 30° | | 1 | π/4 | 45° | | √3 | π/3 | 60° | | 2 | 1.1071 | 63.435° | | 3 | 1.2490 | 71.565° | | ∞ | π/2 | 90° |