Arctangent: Value

set x = arctan (-1).

Then tan x = -1.

x is in (-π/2 ≤ x ≤ π/2).

Draw a right triangle
that satisfies
tan x = -1 and (-π/2 ≤ x ≤ π/2).

-π/2 ≤ x ≤ π/2
So the right triangle should be in
either quadrant I or quadrant IV.

See tan x = -1 (= -1/1).

Tangent is TOA:
Tangent,
Opposite side (-1),
Adjacent side (1).

So draw a right triangle on a coordinate plane
whose opposite side is -1
and whose adjacent side is 1.

Draw the angle x
that starts from the 3 o'clock position.

Find the missing side
by using the Pythagorean theorem:
1² + (-1)² = [hypotenuse]².

Then the hypotenuse is √2.

This is a right triangle
whose sides are 1, -1, and √2.

So this is a 45-45-90 triangle.

So the central angle is, 45º, π/4.

Radian Measure

So π/4 is the answer.