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    Cos 324 Degrees

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

    What is cos 324°?

    Answer

    cos 324° =
    (√5 + 1)/4 ≈ 0.8090

    Angle in radians: 324° = 9π/5. The point of the angle is in quadrant IV, where cosine is positive.

    ≈ — rounded to 4 decimal places.

    cos 324° = cos(360° − 36°) = cos 36° = (√5 + 1)/4

    P(cos 324°, sin 324°) = ((√5 + 1)/4, −√(10 − 2√5)/4)

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

    xyOP

    P(cos 324°, sin 324°) ≈ (0.8090, −0.5878)

    Highlighted: the projection on the x-axis — cosine, x ≈ 0.8090.

    All four functions of 324°
    FunctionExact valueDecimal
    sin 324°−√(10 − 2√5)/4≈ −0.5878
    cos 324°(√5 + 1)/4≈ 0.8090
    tan 324°−√(5 − 2√5)≈ −0.7265
    cot 324°−√(25 + 10√5)/5≈ −1.3764

    Reference angle: cos 36° = (√5 + 1)/4

    See Also

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    https://calculat.io/en/number/trigonometry/cos--324Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--324">Cos 324 Degrees: Cosine of 324° on the Unit Circle</a>Copy
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    Cos 324 Degrees: Cosine of 324° on the Unit Circle. cos 324° = (√5 + 1)/4 ≈ 0.8090. The cosine is the x-coordinate of the point at 324° on the unit circle; 324° reduces to 36°.
    https://calculat.io/en/number/trigonometry/cos--324/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    300°1/2
    306°√(10 − 2√5)/4
    315°√2/2
    324°(√5 + 1)/4
    330°√3/2
    341°≈ 0.9455
    342°√(10 + 2√5)/4
    Recalculate with different values ↑

    FAQ

    What is cos 324°?

    cos 324° = (√5 + 1)/4 ≈ 0.8090

    How are sin 36° and cos 54° related?

    They are equal: sin α = cos(90° − α), and 36° + 54° = 90°. So sin 36° = cos 54° = √(10 − 2√5)/4, cos 36° = sin 54° = (√5 + 1)/4, and tan 36° = cot 54° = √(5 − 2√5).

    Why does a calculator show −0.9147 for cos 324?

    The calculator is in radian mode (RAD): it takes cos 324 as the cosine of 324 radians, cos 324 rad ≈ −0.9147. Switch it to degrees (DEG): cos 324° = (√5 + 1)/4 ≈ 0.8090. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also