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    Cot 72 Degrees

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

    What is cot 72°?

    Answer

    cot 72° =
    √(25 − 10√5)/5 ≈ 0.3249

    Angle in radians: 72° = 2π/5. The point of the angle is in quadrant I, where cotangent is positive.

    ≈ — rounded to 4 decimal places.

    cot 72° = cos 72° / sin 72° = ((√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 72°, sin 72°) ≈ (0.3090, 0.9511)

    C(cot 72°, 1) ≈ (0.3249, 1) — where line OP meets the line y = 1.

    All four functions of 72°
    FunctionExact valueDecimal
    sin 72°√(10 + 2√5)/4≈ 0.9511
    cos 72°(√5 − 1)/4≈ 0.3090
    tan 72°√(5 + 2√5)≈ 3.0777
    cot 72°√(25 − 10√5)/5≈ 0.3249

    See Also

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

    Cotangent of nearby angles

    Anglecot
    69°≈ 0.3839
    70°≈ 0.3640
    71°≈ 0.3443
    72°√(25 − 10√5)/5
    73°≈ 0.3057
    74°≈ 0.2867
    75°2 − √3
    Recalculate with different values ↑

    FAQ

    What is cot 72°?

    cot 72° = √(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 −3.8107 for cot 72?

    The calculator is in radian mode (RAD): it takes cot 72 as the cotangent of 72 radians, cot 72 rad ≈ −3.8107. Switch it to degrees (DEG): cot 72° = √(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