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    Cot 390 Degrees

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

    What is cot 390°?

    Answer

    cot 390° =
    √3 ≈ 1.7321

    Angle in radians: 390° = 13π/6. 390° = 360° + 30° — a full turn plus 30°, quadrant I, where cotangent is positive.

    ≈ — rounded to 4 decimal places.

    cot 390° = cot(390° − 360°) = cot 30°

    cot 390° = cos 390° / sin 390° = (√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 390°, sin 390°) ≈ (0.8660, 0.5)

    C(cot 390°, 1) ≈ (1.7321, 1) — where line OP meets the line y = 1.

    +1 turn: the drawing shows 30°.

    All four functions of 390°
    FunctionExact valueDecimal
    sin 390°1/20.5
    cos 390°√3/2≈ 0.8660
    tan 390°√3/3≈ 0.5774
    cot 390°√3≈ 1.7321

    Reference angle: cot 30° = √3

    See Also

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    https://calculat.io/en/number/trigonometry/cot--390Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--390">Cot 390 Degrees: Cotangent of 390° on the Unit Circle</a>Copy
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    Cot 390 Degrees: Cotangent of 390° on the Unit Circle. cot 390° = √3 ≈ 1.7321. The cotangent is the ratio x/y of the point at 390° on the unit circle; 390° reduces to 30°.
    https://calculat.io/en/number/trigonometry/cot--390/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    345°−2 − √3
    355°≈ −11.4301
    360°undefined
    390°√3
    400°≈ 1.1918
    450°0
    540°undefined
    Recalculate with different values ↑

    FAQ

    What is cot 390°?

    cot 390° = √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 390° = √3 ≈ 1.7321.

    Why does a calculator show 2.1104 for cot 390?

    The calculator is in radian mode (RAD): it takes cot 390 as the cotangent of 390 radians, cot 390 rad ≈ 2.1104. Switch it to degrees (DEG): cot 390° = √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