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    Cos 306 Degrees

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

    What is cos 306°?

    Answer

    cos 306° =
    √(10 − 2√5)/4 ≈ 0.5878

    Angle in radians: 306° = 17π/10. The point of the angle is in quadrant IV, where cosine is positive.

    ≈ — rounded to 4 decimal places.

    cos 306° = cos(360° − 54°) = cos 54° = √(10 − 2√5)/4

    P(cos 306°, sin 306°) = (√(10 − 2√5)/4, −(√5 + 1)/4)

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

    cos 54° = sin 36° = √(1 − cos² 36°) = √(10 − 2√5)/4

    xyOP

    P(cos 306°, sin 306°) ≈ (0.5878, −0.8090)

    Highlighted: the projection on the x-axis — cosine, x ≈ 0.5878.

    All four functions of 306°
    FunctionExact valueDecimal
    sin 306°−(√5 + 1)/4≈ −0.8090
    cos 306°√(10 − 2√5)/4≈ 0.5878
    tan 306°−√(25 + 10√5)/5≈ −1.3764
    cot 306°−√(5 − 2√5)≈ −0.7265

    Reference angle: cos 54° = √(10 − 2√5)/4

    See Also

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    https://calculat.io/en/number/trigonometry/cos--306Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--306">Cos 306 Degrees: Cosine of 306° on the Unit Circle</a>Copy
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    Cos 306 Degrees: Cosine of 306° on the Unit Circle. cos 306° = √(10 − 2√5)/4 ≈ 0.5878. The cosine is the x-coordinate of the point at 306° on the unit circle; 306° reduces to 54°.
    https://calculat.io/en/number/trigonometry/cos--306/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    285°(√6 − √2)/4
    288°(√5 − 1)/4
    300°1/2
    306°√(10 − 2√5)/4
    315°√2/2
    324°(√5 + 1)/4
    330°√3/2
    Recalculate with different values ↑

    FAQ

    What is cos 306°?

    cos 306° = √(10 − 2√5)/4 ≈ 0.5878

    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 −0.3006 for cos 306?

    The calculator is in radian mode (RAD): it takes cos 306 as the cosine of 306 radians, cos 306 rad ≈ −0.3006. Switch it to degrees (DEG): cos 306° = √(10 − 2√5)/4 ≈ 0.5878. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also