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    Sin 150 Degrees

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

    What is sin 150°?

    Answer

    sin 150° =
    1/2 = 0.5

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

    sin 150° = sin(180° − 30°) = sin 30° = 1/2

    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.

    sin 30° = 1/2

    xyOP

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

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

    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: sin 30° = 1/2

    See Also

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    https://calculat.io/en/number/trigonometry/sin--150Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--150">Sin 150 Degrees: Sine of 150° on the Unit Circle</a>Copy
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    Sin 150 Degrees: Sine of 150° on the Unit Circle. sin 150° = 1/2 = 0.5. The sine is the y-coordinate of the point at 150° on the unit circle; 150° reduces to 30°.
    https://calculat.io/en/number/trigonometry/sin--150/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    142°≈ 0.6157
    144°√(10 − 2√5)/4
    145°≈ 0.5736
    150°1/2
    159°≈ 0.3584
    160°≈ 0.3420
    162°(√5 − 1)/4
    Recalculate with different values ↑

    FAQ

    What is sin 150°?

    sin 150° = 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 150° = 1/2 = 0.5.

    Why does a calculator show −0.7149 for sin 150?

    The calculator is in radian mode (RAD): it takes sin 150 as the sine of 150 radians, sin 150 rad ≈ −0.7149. Switch it to degrees (DEG): sin 150° = 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