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    Cos 234 Degrees

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

    What is cos 234°?

    Answer

    cos 234° =
    −√(10 − 2√5)/4 ≈ −0.5878

    Angle in radians: 234° = 13π/10. The point of the angle is in quadrant III, where cosine is negative.

    ≈ — rounded to 4 decimal places.

    cos 234° = cos(180° + 54°) = −cos 54° = −√(10 − 2√5)/4

    P(cos 234°, sin 234°) = (−√(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 234°, sin 234°) ≈ (−0.5878, −0.8090)

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

    All four functions of 234°
    FunctionExact valueDecimal
    sin 234°−(√5 + 1)/4≈ −0.8090
    cos 234°−√(10 − 2√5)/4≈ −0.5878
    tan 234°√(25 + 10√5)/5≈ 1.3764
    cot 234°√(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--234Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--234">Cos 234 Degrees: Cosine of 234° on the Unit Circle</a>Copy
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    Cos 234 Degrees: Cosine of 234° on the Unit Circle. cos 234° = −√(10 − 2√5)/4 ≈ −0.5878. The cosine is the x-coordinate of the point at 234° on the unit circle; 234° reduces to 54°.
    https://calculat.io/en/number/trigonometry/cos--234/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    216°−(√5 + 1)/4
    225°−√2/2
    227°≈ −0.6820
    234°−√(10 − 2√5)/4
    240°−1/2
    252°−(√5 − 1)/4
    255°−(√6 − √2)/4
    Recalculate with different values ↑

    FAQ

    What is cos 234°?

    cos 234° = −√(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 0.0486 for cos 234?

    The calculator is in radian mode (RAD): it takes cos 234 as the cosine of 234 radians, cos 234 rad ≈ 0.0486. Switch it to degrees (DEG): cos 234° = −√(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