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    Cos 252 Degrees

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

    What is cos 252°?

    Answer

    cos 252° =
    −(√5 − 1)/4 ≈ −0.3090

    Angle in radians: 252° = 7π/5. The point of the angle is in quadrant III, where cosine is negative.

    ≈ — rounded to 4 decimal places.

    cos 252° = cos(180° + 72°) = −cos 72° = −(√5 − 1)/4

    P(cos 252°, sin 252°) = (−(√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 252°, sin 252°) ≈ (−0.3090, −0.9511)

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

    All four functions of 252°
    FunctionExact valueDecimal
    sin 252°−√(10 + 2√5)/4≈ −0.9511
    cos 252°−(√5 − 1)/4≈ −0.3090
    tan 252°√(5 + 2√5)≈ 3.0777
    cot 252°√(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--252Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--252">Cos 252 Degrees: Cosine of 252° on the Unit Circle</a>Copy
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    Cos 252 Degrees: Cosine of 252° on the Unit Circle. cos 252° = −(√5 − 1)/4 ≈ −0.3090. The cosine is the x-coordinate of the point at 252° on the unit circle; 252° reduces to 72°.
    https://calculat.io/en/number/trigonometry/cos--252/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    227°≈ −0.6820
    234°−√(10 − 2√5)/4
    240°−1/2
    252°−(√5 − 1)/4
    255°−(√6 − √2)/4
    270°0
    285°(√6 − √2)/4
    Recalculate with different values ↑

    FAQ

    What is cos 252°?

    cos 252° = −(√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 0.7822 for cos 252?

    The calculator is in radian mode (RAD): it takes cos 252 as the cosine of 252 radians, cos 252 rad ≈ 0.7822. Switch it to degrees (DEG): cos 252° = −(√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