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    Cos 72 Degrees

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

    What is cos 72°?

    Answer

    cos 72° =
    (√5 − 1)/4 ≈ 0.3090

    Angle in radians: 72° = 2π/5. The point of the angle is in quadrant I, where cosine is positive.

    ≈ — rounded to 4 decimal places.

    P(cos 72°, sin 72°) = ((√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 72°, sin 72°) ≈ (0.3090, 0.9511)

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

    All four functions of 72°
    FunctionExact valueDecimal
    sin 72°√(10 + 2√5)/4≈ 0.9511
    cos 72°(√5 − 1)/4≈ 0.3090
    tan 72°√(5 + 2√5)≈ 3.0777
    cot 72°√(25 − 10√5)/5≈ 0.3249

    See Also

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

    Cosine of nearby angles

    Anglecos
    69°≈ 0.3584
    70°≈ 0.3420
    71°≈ 0.3256
    72°(√5 − 1)/4
    73°≈ 0.2924
    74°≈ 0.2756
    75°(√6 − √2)/4
    Recalculate with different values ↑

    FAQ

    What is cos 72°?

    cos 72° = (√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 −0.9673 for cos 72?

    The calculator is in radian mode (RAD): it takes cos 72 as the cosine of 72 radians, cos 72 rad ≈ −0.9673. Switch it to degrees (DEG): cos 72° = (√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