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    Tan 120 Degrees

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

    What is tan 120°?

    Answer

    tan 120° =
    −√3 ≈ −1.7321

    Angle in radians: 120° = 2π/3. The point of the angle is in quadrant II, where tangent is negative.

    ≈ — rounded to 4 decimal places.

    tan 120° = tan(180° − 60°) = −tan 60° = −√3

    tan 120° = sin 120° / cos 120° = (√3/2) / (−1/2) = −√3

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

    tan 60° = (√3/2) / (1/2) = √3

    xyOP

    P(cos 120°, sin 120°) ≈ (−0.5, 0.8660)

    T(1, tan 120°) ≈ (1, −1.7321) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

    All four functions of 120°
    FunctionExact valueDecimal
    sin 120°√3/2≈ 0.8660
    cos 120°−1/2−0.5
    tan 120°−√3≈ −1.7321
    cot 120°−√3/3≈ −0.5774

    Reference angle: tan 60° = √3

    See Also

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    https://calculat.io/en/number/trigonometry/tan--120Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--120">Tan 120 Degrees: Tangent of 120° on the Unit Circle</a>Copy
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    Tan 120 Degrees: Tangent of 120° on the Unit Circle. tan 120° = −√3 ≈ −1.7321. The tangent is the ratio y/x of the point at 120° on the unit circle; 120° reduces to 60°.
    https://calculat.io/en/number/trigonometry/tan--120/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    106°≈ −3.4874
    108°−√(5 + 2√5)
    110°≈ −2.7475
    120°−√3
    125°≈ −1.4281
    126°−√(25 + 10√5)/5
    127°≈ −1.3270
    Recalculate with different values ↑

    FAQ

    What is tan 120°?

    tan 120° = −√3 ≈ −1.7321

    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 120° = −√3 ≈ −1.7321.

    Why does a calculator show 0.7131 for tan 120?

    The calculator is in radian mode (RAD): it takes tan 120 as the tangent of 120 radians, tan 120 rad ≈ 0.7131. Switch it to degrees (DEG): tan 120° = −√3 ≈ −1.7321. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also