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    Cos 18 Degrees

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

    What is cos 18°?

    Answer

    cos 18° =
    √(10 + 2√5)/4 ≈ 0.9511

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

    ≈ — rounded to 4 decimal places.

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

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

    cos 18° = √(1 − sin² 18°) = √(10 + 2√5)/4

    xyOP

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

    Highlighted: the projection on the x-axis — cosine, x ≈ 0.9511.

    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

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    https://calculat.io/en/number/trigonometry/cos--18Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--18">Cos 18 Degrees: Cosine of 18° on the Unit Circle</a>Copy
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    Cos 18 Degrees: Cosine of 18° on the Unit Circle. cos 18° = √(10 + 2√5)/4 ≈ 0.9511. The cosine is the x-coordinate of the point at 18° on the unit circle.
    https://calculat.io/en/number/trigonometry/cos--18/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    15°(√6 + √2)/4
    16°≈ 0.9613
    17°≈ 0.9563
    18°√(10 + 2√5)/4
    19°≈ 0.9455
    20°≈ 0.9397
    21°≈ 0.9336
    Recalculate with different values ↑

    FAQ

    What is cos 18°?

    cos 18° = √(10 + 2√5)/4 ≈ 0.9511

    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 0.6603 for cos 18?

    The calculator is in radian mode (RAD): it takes cos 18 as the cosine of 18 radians, cos 18 rad ≈ 0.6603. Switch it to degrees (DEG): cos 18° = √(10 + 2√5)/4 ≈ 0.9511. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also