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) / (1αβ)] 
Arctan difference 
arctan α  arctan β = arctan [(αβ) / (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° 
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