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    Cot 108 Degrees

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

    What is cot 108°?

    Answer

    cot 108° =
    −√(25 − 10√5)/5 ≈ −0.3249

    Angle in radians: 108° = 3π/5. The point of the angle is in quadrant II, where cotangent is negative.

    ≈ — rounded to 4 decimal places.

    cot 108° = cot(180° − 72°) = −cot 72° = −√(25 − 10√5)/5

    cot 108° = cos 108° / sin 108° = (−(√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 108°, sin 108°) ≈ (−0.3090, 0.9511)

    C(cot 108°, 1) ≈ (−0.3249, 1) — where line OP meets the line y = 1.

    All four functions of 108°
    FunctionExact valueDecimal
    sin 108°√(10 + 2√5)/4≈ 0.9511
    cos 108°−(√5 − 1)/4≈ −0.3090
    tan 108°−√(5 + 2√5)≈ −3.0777
    cot 108°−√(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--108Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--108">Cot 108 Degrees: Cotangent of 108° on the Unit Circle</a>Copy
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    Cot 108 Degrees: Cotangent of 108° on the Unit Circle. cot 108° = −√(25 − 10√5)/5 ≈ −0.3249. The cotangent is the ratio x/y of the point at 108° on the unit circle; 108° reduces to 72°.
    https://calculat.io/en/number/trigonometry/cot--108/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    101°≈ −0.1944
    105°√3 − 2
    106°≈ −0.2867
    108°−√(25 − 10√5)/5
    110°≈ −0.3640
    120°−√3/3
    125°≈ −0.7002
    Recalculate with different values ↑

    FAQ

    What is cot 108°?

    cot 108° = −√(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 0.4052 for cot 108?

    The calculator is in radian mode (RAD): it takes cot 108 as the cotangent of 108 radians, cot 108 rad ≈ 0.4052. Switch it to degrees (DEG): cot 108° = −√(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