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    Sin 159 Degrees

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

    What is sin 159°?

    Answer

    sin 159° ≈
    0.3584

    Angle in radians: 159° = 53π/60. The point of the angle is in quadrant II, where sine is positive.

    ≈ — rounded to 4 decimal places. An exact form of sin 159° in square roots exists, but it is unwieldy — nested radicals.

    sin 159° = sin(180° − 21°) = sin 21° ≈ 0.3584

    P(cos 159°, sin 159°) ≈ (−0.9336, 0.3584)

    xyOP

    P(cos 159°, sin 159°) ≈ (−0.9336, 0.3584)

    Highlighted: the projection on the y-axis — sine, y ≈ 0.3584.

    All four functions of 159°
    FunctionExact valueDecimal
    sin 159°—≈ 0.3584
    cos 159°—≈ −0.9336
    tan 159°—≈ −0.3839
    cot 159°—≈ −2.6051

    Reference angle: sin 21° ≈ 0.3584

    See Also

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    https://calculat.io/en/number/trigonometry/sin--159Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--159">Sin 159 Degrees: Sine of 159° on the Unit Circle</a>Copy
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    Sin 159 Degrees: Sine of 159° on the Unit Circle. sin 159° ≈ 0.3584. The sine is the y-coordinate of the point at 159° on the unit circle; 159° reduces to 21°.
    https://calculat.io/en/number/trigonometry/sin--159/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    144°√(10 − 2√5)/4
    145°≈ 0.5736
    150°1/2
    159°≈ 0.3584
    160°≈ 0.3420
    162°(√5 − 1)/4
    164°≈ 0.2756
    Recalculate with different values ↑

    FAQ

    What is sin 159°?

    sin 159° ≈ 0.3584

    Is there an exact value of sin 159°?

    Yes: 159° is a multiple of 3°, and the values of such angles can be written with square roots — but the expression is unwieldy, with nested radicals built from the values of 18° and 15° (3° = 18° − 15°). In practice the decimal is used: sin 159° ≈ 0.3584.

    Why does a calculator show 0.9395 for sin 159?

    The calculator is in radian mode (RAD): it takes sin 159 as the sine of 159 radians, sin 159 rad ≈ 0.9395. Switch it to degrees (DEG): sin 159° ≈ 0.3584. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also