Tangent function, tan(x)

Tangent definition

In a right triangle ABC the tangent of α, tan(α) is defined as the ratio betwween the side opposite to angle α and the side adjacent to the angle α:

tan α = a / b

For example:

a = 5″

b = 10″

tan α = b = 5 / 10 = 0.5

Graph of tangent


Tangent rules

Inverse tangent function

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°

Tangent table