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    Cot 690 Degrees

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

    What is cot 690°?

    Answer

    cot 690° =
    −√3 ≈ −1.7321

    Angle in radians: 690° = 23π/6. 690° = 360° + 330° — a full turn plus 330°, quadrant IV, where cotangent is negative.

    ≈ — rounded to 4 decimal places.

    cot 690° = cot(690° − 360°) = cot 330°

    cot 330° = cot(360° − 30°) = −cot 30° = −√3

    cot 690° = cos 690° / sin 690° = (√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 690°, sin 690°) ≈ (0.8660, −0.5)

    C(cot 690°, 1) ≈ (−1.7321, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

    +1 turn: the drawing shows 330°.

    All four functions of 690°
    FunctionExact valueDecimal
    sin 690°−1/2−0.5
    cos 690°√3/2≈ 0.8660
    tan 690°−√3/3≈ −0.5774
    cot 690°−√3≈ −1.7321

    Reference angle: cot 30° = √3

    See Also

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    https://calculat.io/en/number/trigonometry/cot--690Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--690">Cot 690 Degrees: Cotangent of 690° on the Unit Circle</a>Copy
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    Cot 690 Degrees: Cotangent of 690° on the Unit Circle. cot 690° = −√3 ≈ −1.7321. The cotangent is the ratio x/y of the point at 690° on the unit circle; 690° reduces to 30°.
    https://calculat.io/en/number/trigonometry/cot--690/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    390°√3
    400°≈ 1.1918
    450°0
    540°undefined
    570°√3
    690°−√3
    720°undefined
    Recalculate with different values ↑

    FAQ

    What is cot 690°?

    cot 690° = −√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 690° = −√3 ≈ −1.7321.

    Why does a calculator show −0.4471 for cot 690?

    The calculator is in radian mode (RAD): it takes cot 690 as the cotangent of 690 radians, cot 690 rad ≈ −0.4471. Switch it to degrees (DEG): cot 690° = −√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