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

For example:

arctan 1 = tan^-1 1 = π/4 rad = 45°

Graph of arctan

f(x) = arctan(x)

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