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    Sin 120 Degrees

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

    What is sin 120°?

    Answer

    sin 120° =
    √3/2 ≈ 0.8660

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

    ≈ — rounded to 4 decimal places.

    sin 120° = sin(180° − 60°) = sin 60° = √3/2

    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.

    sin 60° = √(1 − 1/4) = √3/2

    xyOP

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

    Highlighted: the projection on the y-axis — sine, y ≈ 0.8660.

    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: sin 60° = √3/2

    See Also

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    https://calculat.io/en/number/trigonometry/sin--120Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--120">Sin 120 Degrees: Sine of 120° on the Unit Circle</a>Copy
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    Sin 120 Degrees: Sine of 120° on the Unit Circle. sin 120° = √3/2 ≈ 0.8660. The sine is the y-coordinate of the point at 120° on the unit circle; 120° reduces to 60°.
    https://calculat.io/en/number/trigonometry/sin--120/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    106°≈ 0.9613
    108°√(10 + 2√5)/4
    110°≈ 0.9397
    120°√3/2
    125°≈ 0.8192
    126°(√5 + 1)/4
    127°≈ 0.7986
    Recalculate with different values ↑

    FAQ

    What is sin 120°?

    sin 120° = √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: sin 120° = √3/2 ≈ 0.8660.

    Why does a calculator show 0.5806 for sin 120?

    The calculator is in radian mode (RAD): it takes sin 120 as the sine of 120 radians, sin 120 rad ≈ 0.5806. Switch it to degrees (DEG): sin 120° = √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