Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    Cot 18 Degrees

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

    What is cot 18°?

    Answer

    cot 18° =
    √(5 + 2√5) ≈ 3.0777

    Angle in radians: 18° = π/10. The point of the angle is in quadrant I, where cotangent is positive.

    ≈ — rounded to 4 decimal places.

    cot 18° = cos 18° / sin 18° = (√(10 + 2√5)/4) / ((√5 − 1)/4) = √(5 + 2√5)

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

    cot 18° = cos 18° / sin 18° = √(5 + 2√5)

    xyOP

    P(cos 18°, sin 18°) ≈ (0.9511, 0.3090)

    C(cot 18°, 1) ≈ (3.0777, 1) — where line OP meets the line y = 1; C is beyond the drawing, the arrow points to it.

    All four functions of 18°
    FunctionExact valueDecimal
    sin 18°(√5 − 1)/4≈ 0.3090
    cos 18°√(10 + 2√5)/4≈ 0.9511
    tan 18°√(25 − 10√5)/5≈ 0.3249
    cot 18°√(5 + 2√5)≈ 3.0777

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/trigonometry/cot--18Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--18">Cot 18 Degrees: Cotangent of 18° on the Unit Circle</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    Cot 18 Degrees: Cotangent of 18° on the Unit Circle. cot 18° = √(5 + 2√5) ≈ 3.0777. The cotangent is the ratio x/y of the point at 18° on the unit circle.
    https://calculat.io/en/number/trigonometry/cot--18/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    15°2 + √3
    16°≈ 3.4874
    17°≈ 3.2709
    18°√(5 + 2√5)
    19°≈ 2.9042
    20°≈ 2.7475
    21°≈ 2.6051
    Recalculate with different values ↑

    FAQ

    What is cot 18°?

    cot 18° = √(5 + 2√5) ≈ 3.0777

    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 −0.8793 for cot 18?

    The calculator is in radian mode (RAD): it takes cot 18 as the cotangent of 18 radians, cot 18 rad ≈ −0.8793. Switch it to degrees (DEG): cot 18° = √(5 + 2√5) ≈ 3.0777. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also