Arctan of 1

Arcsin, Arccos, Arctan, Arccot

What is arctan(1)?

Answer

arctan(1) =

45° = π/4

Range: arctan x is an angle strictly between −90° and 90°, so the answer is unique.

arctan(1) is the angle α in (−90°, 90°) with tan α = 1.

α = arctan(1) = 45°

P(cos 45°, sin 45°) = (√2/2, √2/2)

T(1, 1) is where line OP meets the line x = 1; highlighted: tan α = 1.

arctan(1) = 45° = π/4

Look in the table for the angle α in (−90°, 90°) with tan α = 1: it is 45°, or π/4 in radians.

The calculator is in radian mode (RAD) and gives the angle in radians: arctan(1) = π/4 ≈ 0.7854 rad. In degrees (DEG) it is 45°.