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.

arctan(−1) = −arctan(1) = −45°

tan(−45°) = −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

arctan is an odd function: arctan(−x) = −arctan x. So arctan(−1) = −arctan(1) = −45°, and this angle lies in the range (−90°, 90°).

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°.