Arctangent function
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° |