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    Sin 9 Degrees

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

    What is sin 9°?

    Answer

    sin 9° ≈
    0.1564

    Angle in radians: 9° = π/20. The point of the angle is in quadrant I, where sine is positive.

    ≈ — rounded to 4 decimal places. An exact form of sin 9° in square roots exists, but it is unwieldy — nested radicals.

    P(cos 9°, sin 9°) ≈ (0.9877, 0.1564)

    xyOP

    P(cos 9°, sin 9°) ≈ (0.9877, 0.1564)

    Highlighted: the projection on the y-axis — sine, y ≈ 0.1564.

    All four functions of 9°
    FunctionExact valueDecimal
    sin 9°—≈ 0.1564
    cos 9°—≈ 0.9877
    tan 9°—≈ 0.1584
    cot 9°—≈ 6.3138

    See Also

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    https://calculat.io/en/number/trigonometry/sin--9Copy
    <a href="https://calculat.io/en/number/trigonometry/sin--9">Sin 9 Degrees: Sine of 9° on the Unit Circle - Calculatio</a>Copy
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    Sin 9 Degrees: Sine of 9° on the Unit Circle. sin 9° ≈ 0.1564. The sine is the y-coordinate of the point at 9° on the unit circle.
    https://calculat.io/en/number/trigonometry/sin--9/generated.jpgCopy

    Sine of nearby angles

    Anglesin
    6°≈ 0.1045
    7°≈ 0.1219
    8°≈ 0.1392
    9°≈ 0.1564
    10°≈ 0.1736
    11°≈ 0.1908
    12°≈ 0.2079
    Recalculate with different values ↑

    FAQ

    What is sin 9°?

    sin 9° ≈ 0.1564

    Is there an exact value of sin 9°?

    Yes: 9° 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 9° ≈ 0.1564.

    Why does a calculator show 0.4121 for sin 9?

    The calculator is in radian mode (RAD): it takes sin 9 as the sine of 9 radians, sin 9 rad ≈ 0.4121. Switch it to degrees (DEG): sin 9° ≈ 0.1564. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also