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    Sin 210 Degrees

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

    What is sin 210°?

    Answer

    sin 210° =
    −1/2 = −0.5

    Angle in radians: 210° = 7π/6. The point of the angle is in quadrant III, where sine is negative.

    sin 210° = sin(180° + 30°) = −sin 30° = −1/2

    P(cos 210°, sin 210°) = (−√3/2, −1/2)

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

    sin 30° = 1/2

    xyOP

    P(cos 210°, sin 210°) ≈ (−0.8660, −0.5)

    Highlighted: the projection on the y-axis — sine, y = −0.5.

    All four functions of 210°
    FunctionExact valueDecimal
    sin 210°−1/2−0.5
    cos 210°−√3/2≈ −0.8660
    tan 210°√3/3≈ 0.5774
    cot 210°√3≈ 1.7321

    Reference angle: sin 30° = 1/2

    See Also

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    https://calculat.io/en/number/trigonometry/sin--210Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--210">Sin 210 Degrees: Sine of 210° on the Unit Circle</a>Copy
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    Sin 210 Degrees: Sine of 210° on the Unit Circle. sin 210° = −1/2 = −0.5. The sine is the y-coordinate of the point at 210° on the unit circle; 210° reduces to 30°.
    https://calculat.io/en/number/trigonometry/sin--210/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    195°−(√6 − √2)/4
    198°−(√5 − 1)/4
    200°≈ −0.3420
    210°−1/2
    211°≈ −0.5150
    215°≈ −0.5736
    216°−√(10 − 2√5)/4
    Recalculate with different values ↑

    FAQ

    What is sin 210°?

    sin 210° = −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: sin 210° = −1/2 = −0.5.

    Why does a calculator show 0.4677 for sin 210?

    The calculator is in radian mode (RAD): it takes sin 210 as the sine of 210 radians, sin 210 rad ≈ 0.4677. Switch it to degrees (DEG): sin 210° = −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