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    Cot 285 Degrees

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

    What is cot 285°?

    Answer

    cot 285° =
    √3 − 2 ≈ −0.2679

    Angle in radians: 285° = 19π/12. The point of the angle is in quadrant IV, where cotangent is negative.

    ≈ — rounded to 4 decimal places.

    cot 285° = cot(360° − 75°) = −cot 75° = √3 − 2

    cot 285° = cos 285° / sin 285° = ((√6 − √2)/4) / (−(√6 + √2)/4) = √3 − 2

    cot 75° = 1 / tan 75° = 1 / (2 + √3) = 2 − √3

    xyOP

    P(cos 285°, sin 285°) ≈ (0.2588, −0.9659)

    C(cot 285°, 1) ≈ (−0.2679, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

    All four functions of 285°
    FunctionExact valueDecimal
    sin 285°−(√6 + √2)/4≈ −0.9659
    cos 285°(√6 − √2)/4≈ 0.2588
    tan 285°−2 − √3≈ −3.7321
    cot 285°√3 − 2≈ −0.2679

    Reference angle: cot 75° = 2 − √3

    See Also

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    https://calculat.io/en/number/trigonometry/cot--285Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--285">Cot 285 Degrees: Cotangent of 285° on the Unit Circle</a>Copy
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    Cot 285 Degrees: Cotangent of 285° on the Unit Circle. cot 285° = √3 − 2 ≈ −0.2679. The cotangent is the ratio x/y of the point at 285° on the unit circle; 285° reduces to 75°.
    https://calculat.io/en/number/trigonometry/cot--285/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    252°√(25 − 10√5)/5
    255°2 − √3
    270°0
    285°√3 − 2
    288°−√(25 − 10√5)/5
    300°−√3/3
    306°−√(5 − 2√5)
    Recalculate with different values ↑

    FAQ

    What is cot 285°?

    cot 285° = √3 − 2 ≈ −0.2679

    How are sin 15° and cos 75° related?

    They are equal: sin α = cos(90° − α), and 15° + 75° = 90°. So sin 15° = cos 75° = (√6 − √2)/4, cos 15° = sin 75° = (√6 + √2)/4, and tan 15° = cot 75° = 2 − √3.

    Why does a calculator show −0.8184 for cot 285?

    The calculator is in radian mode (RAD): it takes cot 285 as the cotangent of 285 radians, cot 285 rad ≈ −0.8184. Switch it to degrees (DEG): cot 285° = √3 − 2 ≈ −0.2679. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also