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    Cot 255 Degrees

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

    What is cot 255°?

    Answer

    cot 255° =
    2 − √3 ≈ 0.2679

    Angle in radians: 255° = 17π/12. The point of the angle is in quadrant III, where cotangent is positive.

    ≈ — rounded to 4 decimal places.

    cot 255° = cot(180° + 75°) = cot 75° = 2 − √3

    cot 255° = cos 255° / sin 255° = (−(√6 − √2)/4) / (−(√6 + √2)/4) = 2 − √3

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

    xyOP

    P(cos 255°, sin 255°) ≈ (−0.2588, −0.9659)

    C(cot 255°, 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 255°
    FunctionExact valueDecimal
    sin 255°−(√6 + √2)/4≈ −0.9659
    cos 255°−(√6 − √2)/4≈ −0.2588
    tan 255°2 + √3≈ 3.7321
    cot 255°2 − √3≈ 0.2679

    Reference angle: cot 75° = 2 − √3

    See Also

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    https://calculat.io/en/number/trigonometry/cot--255Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--255">Cot 255 Degrees: Cotangent of 255° on the Unit Circle</a>Copy
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    Cot 255 Degrees: Cotangent of 255° on the Unit Circle. cot 255° = 2 − √3 ≈ 0.2679. The cotangent is the ratio x/y of the point at 255° on the unit circle; 255° reduces to 75°.
    https://calculat.io/en/number/trigonometry/cot--255/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    234°√(5 − 2√5)
    240°√3/3
    252°√(25 − 10√5)/5
    255°2 − √3
    270°0
    285°√3 − 2
    288°−√(25 − 10√5)/5
    Recalculate with different values ↑

    FAQ

    What is cot 255°?

    cot 255° = 2 − √3 ≈ 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 1.7028 for cot 255?

    The calculator is in radian mode (RAD): it takes cot 255 as the cotangent of 255 radians, cot 255 rad ≈ 1.7028. Switch it to degrees (DEG): cot 255° = 2 − √3 ≈ 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