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    Cot 36 Degrees

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

    What is cot 36°?

    Answer

    cot 36° =
    √(25 + 10√5)/5 ≈ 1.3764

    Angle in radians: 36° = π/5. The point of the angle is in quadrant I, where cotangent is positive.

    ≈ — rounded to 4 decimal places.

    cot 36° = cos 36° / sin 36° = ((√5 + 1)/4) / (√(10 − 2√5)/4) = √(25 + 10√5)/5

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

    cot 36° = cos 36° / sin 36° = √(25 + 10√5)/5

    xyOP

    P(cos 36°, sin 36°) ≈ (0.8090, 0.5878)

    C(cot 36°, 1) ≈ (1.3764, 1) — where line OP meets the line y = 1.

    All four functions of 36°
    FunctionExact valueDecimal
    sin 36°√(10 − 2√5)/4≈ 0.5878
    cos 36°(√5 + 1)/4≈ 0.8090
    tan 36°√(5 − 2√5)≈ 0.7265
    cot 36°√(25 + 10√5)/5≈ 1.3764

    See Also

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    https://calculat.io/en/number/trigonometry/cot--36Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--36">Cot 36 Degrees: Cotangent of 36° on the Unit Circle</a>Copy
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    Cot 36 Degrees: Cotangent of 36° on the Unit Circle. cot 36° = √(25 + 10√5)/5 ≈ 1.3764. The cotangent is the ratio x/y of the point at 36° on the unit circle.
    https://calculat.io/en/number/trigonometry/cot--36/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    33°≈ 1.5399
    34°≈ 1.4826
    35°≈ 1.4281
    36°√(25 + 10√5)/5
    37°≈ 1.3270
    38°≈ 1.2799
    39°≈ 1.2349
    Recalculate with different values ↑

    FAQ

    What is cot 36°?

    cot 36° = √(25 + 10√5)/5 ≈ 1.3764

    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 0.1290 for cot 36?

    The calculator is in radian mode (RAD): it takes cot 36 as the cotangent of 36 radians, cot 36 rad ≈ 0.1290. Switch it to degrees (DEG): cot 36° = √(25 + 10√5)/5 ≈ 1.3764. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also