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    Tan 9 Degrees

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

    What is tan 9°?

    Answer

    tan 9° ≈
    0.1584

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

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

    tan 9° = sin 9° / cos 9° ≈ 0.1584

    xyOP

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

    T(1, tan 9°) ≈ (1, 0.1584) — where line OP meets the line x = 1.

    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/tan--9Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--9">Tan 9 Degrees: Tangent of 9° on the Unit Circle - Calculatio</a>Copy
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    Tan 9 Degrees: Tangent of 9° on the Unit Circle. tan 9° ≈ 0.1584. The tangent is the ratio y/x of the point at 9° on the unit circle.
    https://calculat.io/en/number/trigonometry/tan--9/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    6°≈ 0.1051
    7°≈ 0.1228
    8°≈ 0.1405
    9°≈ 0.1584
    10°≈ 0.1763
    11°≈ 0.1944
    12°≈ 0.2126
    Recalculate with different values ↑

    FAQ

    What is tan 9°?

    tan 9° ≈ 0.1584

    Is there an exact value of tan 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: tan 9° ≈ 0.1584.

    Why does a calculator show −0.4523 for tan 9?

    The calculator is in radian mode (RAD): it takes tan 9 as the tangent of 9 radians, tan 9 rad ≈ −0.4523. Switch it to degrees (DEG): tan 9° ≈ 0.1584. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also