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    Cos 288 Degrees

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

    What is cos 288°?

    Answer

    cos 288° =
    (√5 − 1)/4 ≈ 0.3090

    Angle in radians: 288° = 8π/5. The point of the angle is in quadrant IV, where cosine is positive.

    ≈ — rounded to 4 decimal places.

    cos 288° = cos(360° − 72°) = cos 72° = (√5 − 1)/4

    P(cos 288°, sin 288°) = ((√5 − 1)/4, −√(10 + 2√5)/4)

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

    cos 72° = 2 cos² 36° − 1 = (√5 − 1)/4

    xyOP

    P(cos 288°, sin 288°) ≈ (0.3090, −0.9511)

    Highlighted: the projection on the x-axis — cosine, x ≈ 0.3090.

    All four functions of 288°
    FunctionExact valueDecimal
    sin 288°−√(10 + 2√5)/4≈ −0.9511
    cos 288°(√5 − 1)/4≈ 0.3090
    tan 288°−√(5 + 2√5)≈ −3.0777
    cot 288°−√(25 − 10√5)/5≈ −0.3249

    Reference angle: cos 72° = (√5 − 1)/4

    See Also

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    https://calculat.io/en/number/trigonometry/cos--288Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--288">Cos 288 Degrees: Cosine of 288° on the Unit Circle</a>Copy
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    Cos 288 Degrees: Cosine of 288° on the Unit Circle. cos 288° = (√5 − 1)/4 ≈ 0.3090. The cosine is the x-coordinate of the point at 288° on the unit circle; 288° reduces to 72°.
    https://calculat.io/en/number/trigonometry/cos--288/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    255°−(√6 − √2)/4
    270°0
    285°(√6 − √2)/4
    288°(√5 − 1)/4
    300°1/2
    306°√(10 − 2√5)/4
    315°√2/2
    Recalculate with different values ↑

    FAQ

    What is cos 288°?

    cos 288° = (√5 − 1)/4 ≈ 0.3090

    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 0.5178 for cos 288?

    The calculator is in radian mode (RAD): it takes cos 288 as the cosine of 288 radians, cos 288 rad ≈ 0.5178. Switch it to degrees (DEG): cos 288° = (√5 − 1)/4 ≈ 0.3090. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also