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    Cos 240 Degrees

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

    What is cos 240°?

    Answer

    cos 240° =
    −1/2 = −0.5

    Angle in radians: 240° = 4π/3. The point of the angle is in quadrant III, where cosine is negative.

    cos 240° = cos(180° + 60°) = −cos 60° = −1/2

    P(cos 240°, sin 240°) = (−1/2, −√3/2)

    Half of an equilateral triangle with side 1: the hypotenuse is 1 and the leg opposite 30° is 1/2.

    cos 60° = 1/2

    xyOP

    P(cos 240°, sin 240°) ≈ (−0.5, −0.8660)

    Highlighted: the projection on the x-axis — cosine, x = −0.5.

    All four functions of 240°
    FunctionExact valueDecimal
    sin 240°−√3/2≈ −0.8660
    cos 240°−1/2−0.5
    tan 240°√3≈ 1.7321
    cot 240°√3/3≈ 0.5774

    Reference angle: cos 60° = 1/2

    See Also

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    https://calculat.io/en/number/trigonometry/cos--240Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--240">Cos 240 Degrees: Cosine of 240° on the Unit Circle</a>Copy
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    Cos 240 Degrees: Cosine of 240° on the Unit Circle. cos 240° = −1/2 = −0.5. The cosine is the x-coordinate of the point at 240° on the unit circle; 240° reduces to 60°.
    https://calculat.io/en/number/trigonometry/cos--240/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    225°−√2/2
    227°≈ −0.6820
    234°−√(10 − 2√5)/4
    240°−1/2
    252°−(√5 − 1)/4
    255°−(√6 − √2)/4
    270°0
    Recalculate with different values ↑

    FAQ

    What is cos 240°?

    cos 240° = −1/2 = −0.5

    How to remember sin 30°, sin 45° and sin 60°?

    Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: cos 240° = −1/2 = −0.5.

    Why does a calculator show 0.3258 for cos 240?

    The calculator is in radian mode (RAD): it takes cos 240 as the cosine of 240 radians, cos 240 rad ≈ 0.3258. Switch it to degrees (DEG): cos 240° = −1/2 = −0.5. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also