Arccot of −√3

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arccot(−√3)?

Answer

arccot(−√3) =
150° = 5π/6

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

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

arccot(−√3) = 180° − arccot(√3) = 180° − 30° = 150°

cot 150° = −√3 ✓

xyOPC

α = arccot(−√3) = 150°

P(cos 150°, sin 150°) = (−√3/2, 1/2)

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

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)?

arccot(−√3) = 150° = 5π/6

Why is arccot(−√3) = 150° and not −30°?

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) = 180° − arccot(√3) = 180° − 30° = 150°. The angle −30° 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) = −30°?

They use a different range for arccot, (−90°, 90°], and compute arccot x = arctan(1/x): arctan(−√3/3) = −30°. This page follows the school convention, the range (0°, 180°) with arccot x = 90° − arctan x, so arccot(−√3) = 150°. The two answers differ by exactly 180° and have the same cotangent.

See Also