Arctan of −√3/3

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arctan(−√3/3)?

Answer

arctan(−√3/3) =
−30° = −π/6

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

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

arctan(−√3/3) = −arctan(√3/3) = −30°

tan(−30°) = −√3/3 ✓

xyOP

α = arctan(−√3/3) = −30°

P(cos(−30°), sin(−30°)) = (√3/2, −1/2)

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

All four inverse functions of −√3/3
FunctionDegreesRadians
arcsin(−√3/3)≈ −35.2644°≈ −0.6155
arccos(−√3/3)≈ 125.2644°≈ 2.1863
arctan(−√3/3)−30°−π/6
arccot(−√3/3)120°2π/3

See Also

Recalculate with different values ↑

Arctangent of nearby values

xarctan x
−4/3≈ −53.1301°
−1−45° = −π/4
−4/5≈ −38.6598°
−√3/3−30° = −π/6
−0.3≈ −16.6992°
00° = 0
0.1≈ 5.7106°

FAQ

What is arctan(−√3/3)?

arctan(−√3/3) = −30° = −π/6

Why is arctan(−√3/3) = −30°?

arctan is an odd function: arctan(−x) = −arctan x. So arctan(−√3/3) = −arctan(√3/3) = −30°, and this angle lies in the range (−90°, 90°).

Why does a calculator show −0.5236 for arctan(−√3/3)?

The calculator is in radian mode (RAD) and gives the angle in radians: arctan(−√3/3) = −π/6 ≈ −0.5236 rad. In degrees (DEG) it is −30°.

See Also