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    Cot 150 Degrees

    Sin, Cos, Tan, Cot of an Angle
    Function
    Angle (°)

    What is cot 150°?

    Answer

    cot 150° =
    −√3 ≈ −1.7321

    Angle in radians: 150° = 5π/6. The point of the angle is in quadrant II, where cotangent is negative.

    ≈ — rounded to 4 decimal places.

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

    cot 150° = cos 150° / sin 150° = (−√3/2) / (1/2) = −√3

    Half of an equilateral triangle with side 1: the hypotenuse is 1 and the leg opposite 30° is 1/2.

    cot 30° = (√3/2) / (1/2) = √3

    xyOP

    P(cos 150°, sin 150°) ≈ (−0.8660, 0.5)

    C(cot 150°, 1) ≈ (−1.7321, 1) — where line OP meets the line y = 1.

    All four functions of 150°
    FunctionExact valueDecimal
    sin 150°1/20.5
    cos 150°−√3/2≈ −0.8660
    tan 150°−√3/3≈ −0.5774
    cot 150°−√3≈ −1.7321

    Reference angle: cot 30° = √3

    See Also

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    https://calculat.io/en/number/trigonometry/cot--150Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--150">Cot 150 Degrees: Cotangent of 150° on the Unit Circle</a>Copy
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    Cot 150 Degrees: Cotangent of 150° on the Unit Circle. cot 150° = −√3 ≈ −1.7321. The cotangent is the ratio x/y of the point at 150° on the unit circle; 150° reduces to 30°.
    https://calculat.io/en/number/trigonometry/cot--150/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    142°≈ −1.2799
    144°−√(25 + 10√5)/5
    145°≈ −1.4281
    150°−√3
    159°≈ −2.6051
    160°≈ −2.7475
    162°−√(5 + 2√5)
    Recalculate with different values ↑

    FAQ

    What is cot 150°?

    cot 150° = −√3 ≈ −1.7321

    How to remember sin 30°, sin 45° and sin 60°?

    Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: cot 150° = −√3 ≈ −1.7321.

    Why does a calculator show −0.9781 for cot 150?

    The calculator is in radian mode (RAD): it takes cot 150 as the cotangent of 150 radians, cot 150 rad ≈ −0.9781. Switch it to degrees (DEG): cot 150° = −√3 ≈ −1.7321. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also