Arccot of −2

Arcsin, Arccos, Arctan, Arccot
Function
x

What is arccot(−2)?

Answer

arccot(−2) ≈
153.4349° ≈ 2.6779 rad

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

≈ — the value is not a table one; rounded to 4 decimal places.

arccot(−2) is the angle α in (0°, 180°) with cot α = −2.

arccot(−2) = 180° − arccot(2) ≈ 180° − 26.5651° = 153.4349°

cot 153.4349° ≈ −2.0000

xyOPC

α = arccot(−2) ≈ 153.4349°

P ≈ (−0.8944, 0.4472)

C(−2, 1) is where line OP meets the line y = 1; highlighted: cot α = −2.

All four inverse functions of −2
FunctionDegreesRadians
arcsin(−2)does not exist—
arccos(−2)does not exist—
arctan(−2)≈ −63.4349°≈ −1.1071
arccot(−2)≈ 153.4349°≈ 2.6779

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(−2)?

arccot(−2) ≈ 153.4349° ≈ 2.6779 rad

Why is arccot(−2) ≈ 153.4349° and not −26.5651°?

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(−2) = 180° − arccot(2) ≈ 180° − 26.5651° = 153.4349°. The angle −26.5651° 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(−2) ≈ −26.5651°?

They use a different range for arccot, (−90°, 90°], and compute arccot x = arctan(1/x): arctan(−1/2) ≈ −26.5651°. This page follows the school convention, the range (0°, 180°) with arccot x = 90° − arctan x, so arccot(−2) ≈ 153.4349°. The two answers differ by exactly 180° and have the same cotangent.

See Also