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    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

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    https://calculat.io/en/number/inverse-trigonometry/arccot---1Copy
    <a href="https://calculat.io/en/number/inverse-trigonometry/arccot---1">Arccot of −1 (Inverse Cotangent) in Degrees and Radians</a>Copy
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    Arccot of −1 (Inverse Cotangent) in Degrees and Radians. arccot(−1) = 135° = 3π/4: the angle in (0°, 180°) whose cotangent is −1. With the check and the unit circle.
    https://calculat.io/en/number/inverse-trigonometry/arccot---1/generated.jpgCopy

    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°
    Recalculate with different values ↑

    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