Arctan of −√3

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arctan(−√3)?

Answer

arctan(−√3) =
−60° = −π/3

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

arctan(−√3) is the angle α in (−90°, 90°) with tan α = −√3.

arctan(−√3) = −arctan(√3) = −60°

tan(−60°) = −√3 ✓

xyOPT

α = arctan(−√3) = −60°

P(cos(−60°), sin(−60°)) = (1/2, −√3/2)

T(1, −√3) is where line OP meets the line x = 1; highlighted: tan α = −√3.

All four inverse functions of −√3
FunctionDegreesRadians
arcsin(−√3)does not exist—
arccos(−√3)does not exist—
arctan(−√3)−60°−π/3
arccot(−√3)150°5π/6

See Also

Recalculate with different values ↑

Arctangent of nearby values

xarctan x
−3≈ −71.5651°
−2≈ −63.4349°
−√3−60° = −π/3
−4/3≈ −53.1301°
−1−45° = −π/4
−4/5≈ −38.6598°
−√3/3−30° = −π/6

FAQ

What is arctan(−√3)?

arctan(−√3) = −60° = −π/3

Why is arctan(−√3) = −60°?

arctan is an odd function: arctan(−x) = −arctan x. So arctan(−√3) = −arctan(√3) = −60°, and this angle lies in the range (−90°, 90°).

Why does a calculator show −1.0472 for arctan(−√3)?

The calculator is in radian mode (RAD) and gives the angle in radians: arctan(−√3) = −π/3 ≈ −1.0472 rad. In degrees (DEG) it is −60°.

See Also