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    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

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    https://calculat.io/en/number/inverse-trigonometry/arccot---sqrt3Copy
    <a href="https://calculat.io/en/number/inverse-trigonometry/arccot---sqrt3">Arccot of −√3 (Inverse Cotangent) in Degrees and Radians</a>Copy
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    Arccot of −√3 (Inverse Cotangent) in Degrees and Radians. arccot(−√3) = 150° = 5π/6: the angle in (0°, 180°) whose cotangent is −√3. With the check and the unit circle.
    https://calculat.io/en/number/inverse-trigonometry/arccot---sqrt3/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(−√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