Arccot of −√3/3

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arccot(−√3/3)?

Answer

arccot(−√3/3) =
120° = 2π/3

Range: arccot x is an angle strictly between 0° and 180°, so the answer is unique.

arccot(−√3/3) is the angle α in (0°, 180°) with cot α = −√3/3.

arccot(−√3/3) = 180° − arccot(√3/3) = 180° − 60° = 120°

cot 120° = −√3/3 ✓

xyOP

α = arccot(−√3/3) = 120°

P(cos 120°, sin 120°) = (−1/2, √3/2)

C(−√3/3, 1) is where line OP meets the line y = 1; highlighted: cot 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 ↑

Arccotangent of nearby values

xarccot x
−2≈ 153.4349°
−√3150° = 5π/6
−1135° = 3π/4
−√3/3120° = 2π/3
090° = π/2
0.3≈ 73.3008°
1/2≈ 63.4349°

FAQ

What is arccot(−√3/3)?

arccot(−√3/3) = 120° = 2π/3

Why is arccot(−√3/3) = 120° and not −60°?

The range of arccot is strictly between 0° and 180°: there are no negative angles in it. A negative x gives an angle greater than 90°: arccot(−√3/3) = 180° − arccot(√3/3) = 180° − 60° = 120°. The angle −60° differs from the answer by exactly 180° and has the same cotangent, but it lies outside the range: calculators that use the other convention, (−90°, 90°], give it.

Why do some calculators give arccot(−√3/3) = −60°?

They use a different range for arccot, (−90°, 90°], and compute arccot x = arctan(1/x): arctan(−√3) = −60°. This page follows the school convention, the range (0°, 180°) with arccot x = 90° − arctan x, so arccot(−√3/3) = 120°. The two answers differ by exactly 180° and have the same cotangent.

See Also