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    Tan 330 Degrees

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

    What is tan 330°?

    Answer

    tan 330° =
    −√3/3 ≈ −0.5774

    Angle in radians: 330° = 11π/6. The point of the angle is in quadrant IV, where tangent is negative.

    ≈ — rounded to 4 decimal places.

    tan 330° = tan(360° − 30°) = −tan 30° = −√3/3

    tan 330° = sin 330° / cos 330° = (−1/2) / (√3/2) = −√3/3

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

    tan 30° = (1/2) / (√3/2) = 1/√3 = √3/3

    xyOP

    P(cos 330°, sin 330°) ≈ (0.8660, −0.5)

    T(1, tan 330°) ≈ (1, −0.5774) — where line OP meets the line x = 1.

    All four functions of 330°
    FunctionExact valueDecimal
    sin 330°−1/2−0.5
    cos 330°√3/2≈ 0.8660
    tan 330°−√3/3≈ −0.5774
    cot 330°−√3≈ −1.7321

    Reference angle: tan 30° = √3/3

    See Also

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    https://calculat.io/en/number/trigonometry/tan--330Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--330">Tan 330 Degrees: Tangent of 330° on the Unit Circle</a>Copy
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    Tan 330 Degrees: Tangent of 330° on the Unit Circle. tan 330° = −√3/3 ≈ −0.5774. The tangent is the ratio y/x of the point at 330° on the unit circle; 330° reduces to 30°.
    https://calculat.io/en/number/trigonometry/tan--330/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    306°−√(25 + 10√5)/5
    315°−1
    324°−√(5 − 2√5)
    330°−√3/3
    341°≈ −0.3443
    342°−√(25 − 10√5)/5
    345°√3 − 2
    Recalculate with different values ↑

    FAQ

    What is tan 330°?

    tan 330° = −√3/3 ≈ −0.5774

    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: tan 330° = −√3/3 ≈ −0.5774.

    Why does a calculator show 0.1336 for tan 330?

    The calculator is in radian mode (RAD): it takes tan 330 as the tangent of 330 radians, tan 330 rad ≈ 0.1336. Switch it to degrees (DEG): tan 330° = −√3/3 ≈ −0.5774. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also