Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    Cos 120 Degrees

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

    What is cos 120°?

    Answer

    cos 120° =
    −1/2 = −0.5

    Angle in radians: 120° = 2π/3. The point of the angle is in quadrant II, where cosine is negative.

    cos 120° = cos(180° − 60°) = −cos 60° = −1/2

    P(cos 120°, sin 120°) = (−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 120°, sin 120°) ≈ (−0.5, 0.8660)

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

    All four functions of 120°
    FunctionExact valueDecimal
    sin 120°√3/2≈ 0.8660
    cos 120°−1/2−0.5
    tan 120°−√3≈ −1.7321
    cot 120°−√3/3≈ −0.5774

    Reference angle: cos 60° = 1/2

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/trigonometry/cos--120Copy
    <a href="https://calculat.io/en/number/trigonometry/cos--120">Cos 120 Degrees: Cosine of 120° on the Unit Circle</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    Cos 120 Degrees: Cosine of 120° on the Unit Circle. cos 120° = −1/2 = −0.5. The cosine is the x-coordinate of the point at 120° on the unit circle; 120° reduces to 60°.
    https://calculat.io/en/number/trigonometry/cos--120/generated.jpgCopy

    Cosine of nearby angles

    Anglecos
    106°≈ −0.2756
    108°−(√5 − 1)/4
    110°≈ −0.3420
    120°−1/2
    125°≈ −0.5736
    126°−√(10 − 2√5)/4
    127°≈ −0.6018
    Recalculate with different values ↑

    FAQ

    What is cos 120°?

    cos 120° = −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 120° = −1/2 = −0.5.

    Why does a calculator show 0.8142 for cos 120?

    The calculator is in radian mode (RAD): it takes cos 120 as the cosine of 120 radians, cos 120 rad ≈ 0.8142. Switch it to degrees (DEG): cos 120° = −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