Arccot of −1

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arccot(−1)?

Answer

arccot(−1) =
135° = 3π/4

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

arccot(−1) is the angle α in (0°, 180°) with cot α = −1.

arccot(−1) = 180° − arccot(1) = 180° − 45° = 135°

cot 135° = −1 ✓

xyOPC

α = arccot(−1) = 135°

P(cos 135°, sin 135°) = (−√2/2, √2/2)

C(−1, 1) is where line OP meets the line y = 1; highlighted: cot α = −1.

All four inverse functions of −1
FunctionDegreesRadians
arcsin(−1)−90°−π/2
arccos(−1)180°π
arctan(−1)−45°−π/4
arccot(−1)135°3π/4

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(−1)?

arccot(−1) = 135° = 3π/4

Why is arccot(−1) = 135° and not −45°?

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(−1) = 180° − arccot(1) = 180° − 45° = 135°. The angle −45° 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(−1) = −45°?

They use a different range for arccot, (−90°, 90°], and compute arccot x = arctan(1/x): arctan(−1) = −45°. This page follows the school convention, the range (0°, 180°) with arccot x = 90° − arctan x, so arccot(−1) = 135°. The two answers differ by exactly 180° and have the same cotangent.

See Also