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    Cot 120 Degrees

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

    What is cot 120°?

    Answer

    cot 120° =
    −√3/3 ≈ −0.5774

    Angle in radians: 120° = 2π/3. The point of the angle is in quadrant II, where cotangent is negative.

    ≈ — rounded to 4 decimal places.

    cot 120° = cot(180° − 60°) = −cot 60° = −√3/3

    cot 120° = cos 120° / sin 120° = (−1/2) / (√3/2) = −√3/3

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

    cot 60° = (1/2) / (√3/2) = 1/√3 = √3/3

    xyOP

    P(cos 120°, sin 120°) ≈ (−0.5, 0.8660)

    C(cot 120°, 1) ≈ (−0.5774, 1) — where line OP meets the line y = 1.

    All four functions of 120°
    FunctionExact valueDecimal
    sin 120°√3/2≈ 0.8660
    cos 120°−1/2−0.5
    tan 120°−√3≈ −1.7321
    cot 120°−√3/3≈ −0.5774

    Reference angle: cot 60° = √3/3

    See Also

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    https://calculat.io/en/number/trigonometry/cot--120Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--120">Cot 120 Degrees: Cotangent of 120° on the Unit Circle</a>Copy
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    Cot 120 Degrees: Cotangent of 120° on the Unit Circle. cot 120° = −√3/3 ≈ −0.5774. The cotangent is the ratio x/y of the point at 120° on the unit circle; 120° reduces to 60°.
    https://calculat.io/en/number/trigonometry/cot--120/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    106°≈ −0.2867
    108°−√(25 − 10√5)/5
    110°≈ −0.3640
    120°−√3/3
    125°≈ −0.7002
    126°−√(5 − 2√5)
    127°≈ −0.7536
    Recalculate with different values ↑

    FAQ

    What is cot 120°?

    cot 120° = −√3/3 ≈ −0.5774

    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 120° = −√3/3 ≈ −0.5774.

    Why does a calculator show 1.4023 for cot 120?

    The calculator is in radian mode (RAD): it takes cot 120 as the cotangent of 120 radians, cot 120 rad ≈ 1.4023. Switch it to degrees (DEG): cot 120° = −√3/3 ≈ −0.5774. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also