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    Cot 54 Degrees

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

    What is cot 54°?

    Answer

    cot 54° =
    √(5 − 2√5) ≈ 0.7265

    Angle in radians: 54° = 3π/10. The point of the angle is in quadrant I, where cotangent is positive.

    ≈ — rounded to 4 decimal places.

    cot 54° = cos 54° / sin 54° = (√(10 − 2√5)/4) / ((√5 + 1)/4) = √(5 − 2√5)

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

    cot 54° = tan 36° = sin 36° / cos 36° = √(5 − 2√5)

    xyOP

    P(cos 54°, sin 54°) ≈ (0.5878, 0.8090)

    C(cot 54°, 1) ≈ (0.7265, 1) — where line OP meets the line y = 1.

    All four functions of 54°
    FunctionExact valueDecimal
    sin 54°(√5 + 1)/4≈ 0.8090
    cos 54°√(10 − 2√5)/4≈ 0.5878
    tan 54°√(25 + 10√5)/5≈ 1.3764
    cot 54°√(5 − 2√5)≈ 0.7265

    See Also

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    https://calculat.io/en/number/trigonometry/cot--54Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--54">Cot 54 Degrees: Cotangent of 54° on the Unit Circle</a>Copy
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    Cot 54 Degrees: Cotangent of 54° on the Unit Circle. cot 54° = √(5 − 2√5) ≈ 0.7265. The cotangent is the ratio x/y of the point at 54° on the unit circle.
    https://calculat.io/en/number/trigonometry/cot--54/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    51°≈ 0.8098
    52°≈ 0.7813
    53°≈ 0.7536
    54°√(5 − 2√5)
    55°≈ 0.7002
    56°≈ 0.6745
    57°≈ 0.6494
    Recalculate with different values ↑

    FAQ

    What is cot 54°?

    cot 54° = √(5 − 2√5) ≈ 0.7265

    How are sin 36° and cos 54° related?

    They are equal: sin α = cos(90° − α), and 36° + 54° = 90°. So sin 36° = cos 54° = √(10 − 2√5)/4, cos 36° = sin 54° = (√5 + 1)/4, and tan 36° = cot 54° = √(5 − 2√5).

    Why does a calculator show 1.4841 for cot 54?

    The calculator is in radian mode (RAD): it takes cot 54 as the cotangent of 54 radians, cot 54 rad ≈ 1.4841. Switch it to degrees (DEG): cot 54° = √(5 − 2√5) ≈ 0.7265. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also