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    Sin 240 Degrees

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

    What is sin 240°?

    Answer

    sin 240° =
    −√3/2 ≈ −0.8660

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

    ≈ — rounded to 4 decimal places.

    sin 240° = sin(180° + 60°) = −sin 60° = −√3/2

    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.

    sin 60° = √(1 − 1/4) = √3/2

    xyOP

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

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

    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: sin 60° = √3/2

    See Also

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    https://calculat.io/en/number/trigonometry/sin--240Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--240">Sin 240 Degrees: Sine of 240° on the Unit Circle</a>Copy
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    Sin 240 Degrees: Sine of 240° on the Unit Circle. sin 240° = −√3/2 ≈ −0.8660. The sine is the y-coordinate of the point at 240° on the unit circle; 240° reduces to 60°.
    https://calculat.io/en/number/trigonometry/sin--240/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    225°−√2/2
    227°≈ −0.7314
    234°−(√5 + 1)/4
    240°−√3/2
    252°−√(10 + 2√5)/4
    255°−(√6 + √2)/4
    270°−1
    Recalculate with different values ↑

    FAQ

    What is sin 240°?

    sin 240° = −√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 240° = −√3/2 ≈ −0.8660.

    Why does a calculator show 0.9454 for sin 240?

    The calculator is in radian mode (RAD): it takes sin 240 as the sine of 240 radians, sin 240 rad ≈ 0.9454. Switch it to degrees (DEG): sin 240° = −√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