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    Cos 150 Degrees

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

    What is cos 150°?

    Answer

    cos 150° =
    −√3/2 ≈ −0.8660

    Angle in radians: 150° = 5π/6. The point of the angle is in quadrant II, where cosine is negative.

    ≈ — rounded to 4 decimal places.

    cos 150° = cos(180° − 30°) = −cos 30° = −√3/2

    P(cos 150°, sin 150°) = (−√3/2, 1/2)

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

    cos 30° = √(1 − 1/4) = √3/2

    xyOP

    P(cos 150°, sin 150°) ≈ (−0.8660, 0.5)

    Highlighted: the projection on the x-axis — cosine, x ≈ −0.8660.

    All four functions of 150°
    FunctionExact valueDecimal
    sin 150°1/20.5
    cos 150°−√3/2≈ −0.8660
    tan 150°−√3/3≈ −0.5774
    cot 150°−√3≈ −1.7321

    Reference angle: cos 30° = √3/2

    See Also

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    https://calculat.io/en/number/trigonometry/cos--150Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--150">Cos 150 Degrees: Cosine of 150° on the Unit Circle</a>Copy
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    Cos 150 Degrees: Cosine of 150° on the Unit Circle. cos 150° = −√3/2 ≈ −0.8660. The cosine is the x-coordinate of the point at 150° on the unit circle; 150° reduces to 30°.
    https://calculat.io/en/number/trigonometry/cos--150/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    142°≈ −0.7880
    144°−(√5 + 1)/4
    145°≈ −0.8192
    150°−√3/2
    159°≈ −0.9336
    160°≈ −0.9397
    162°−√(10 + 2√5)/4
    Recalculate with different values ↑

    FAQ

    What is cos 150°?

    cos 150° = −√3/2 ≈ −0.8660

    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 150° = −√3/2 ≈ −0.8660.

    Why does a calculator show 0.6993 for cos 150?

    The calculator is in radian mode (RAD): it takes cos 150 as the cosine of 150 radians, cos 150 rad ≈ 0.6993. Switch it to degrees (DEG): cos 150° = −√3/2 ≈ −0.8660. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also