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    Cot 252 Degrees

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

    What is cot 252°?

    Answer

    cot 252° =
    √(25 − 10√5)/5 ≈ 0.3249

    Angle in radians: 252° = 7π/5. The point of the angle is in quadrant III, where cotangent is positive.

    ≈ — rounded to 4 decimal places.

    cot 252° = cot(180° + 72°) = cot 72° = √(25 − 10√5)/5

    cot 252° = cos 252° / sin 252° = (−(√5 − 1)/4) / (−√(10 + 2√5)/4) = √(25 − 10√5)/5

    Regular pentagon (golden ratio): cos 36° = (√5 + 1)/4.

    cot 72° = tan 18° = sin 18° / cos 18° = √(25 − 10√5)/5

    xyOP

    P(cos 252°, sin 252°) ≈ (−0.3090, −0.9511)

    C(cot 252°, 1) ≈ (0.3249, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

    All four functions of 252°
    FunctionExact valueDecimal
    sin 252°−√(10 + 2√5)/4≈ −0.9511
    cos 252°−(√5 − 1)/4≈ −0.3090
    tan 252°√(5 + 2√5)≈ 3.0777
    cot 252°√(25 − 10√5)/5≈ 0.3249

    Reference angle: cot 72° = √(25 − 10√5)/5

    See Also

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    https://calculat.io/en/number/trigonometry/cot--252Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--252">Cot 252 Degrees: Cotangent of 252° on the Unit Circle</a>Copy
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    Cot 252 Degrees: Cotangent of 252° on the Unit Circle. cot 252° = √(25 − 10√5)/5 ≈ 0.3249. The cotangent is the ratio x/y of the point at 252° on the unit circle; 252° reduces to 72°.
    https://calculat.io/en/number/trigonometry/cot--252/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    227°≈ 0.9325
    234°√(5 − 2√5)
    240°√3/3
    252°√(25 − 10√5)/5
    255°2 − √3
    270°0
    285°√3 − 2
    Recalculate with different values ↑

    FAQ

    What is cot 252°?

    cot 252° = √(25 − 10√5)/5 ≈ 0.3249

    How are sin 18° and cos 72° related?

    They are equal: sin α = cos(90° − α), and 18° + 72° = 90°. So sin 18° = cos 72° = (√5 − 1)/4, cos 18° = sin 72° = √(10 + 2√5)/4, and tan 18° = cot 72° = √(25 − 10√5)/5.

    Why does a calculator show 1.2555 for cot 252?

    The calculator is in radian mode (RAD): it takes cot 252 as the cotangent of 252 radians, cot 252 rad ≈ 1.2555. Switch it to degrees (DEG): cot 252° = √(25 − 10√5)/5 ≈ 0.3249. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also