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    Tan 240 Degrees

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

    What is tan 240°?

    Answer

    tan 240° =
    √3 ≈ 1.7321

    Angle in radians: 240° = 4π/3. The point of the angle is in quadrant III, where tangent is positive.

    ≈ — rounded to 4 decimal places.

    tan 240° = tan(180° + 60°) = tan 60° = √3

    tan 240° = sin 240° / cos 240° = (−√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 240°, sin 240°) ≈ (−0.5, −0.8660)

    T(1, tan 240°) ≈ (1, 1.7321) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

    All four functions of 240°
    FunctionExact valueDecimal
    sin 240°−√3/2≈ −0.8660
    cos 240°−1/2−0.5
    tan 240°√3≈ 1.7321
    cot 240°√3/3≈ 0.5774

    Reference angle: tan 60° = √3

    See Also

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    https://calculat.io/en/number/trigonometry/tan--240Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--240">Tan 240 Degrees: Tangent of 240° on the Unit Circle</a>Copy
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    Tan 240 Degrees: Tangent of 240° on the Unit Circle. tan 240° = √3 ≈ 1.7321. The tangent is the ratio y/x of the point at 240° on the unit circle; 240° reduces to 60°.
    https://calculat.io/en/number/trigonometry/tan--240/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    225°1
    227°≈ 1.0724
    234°√(25 + 10√5)/5
    240°√3
    252°√(5 + 2√5)
    255°2 + √3
    270°undefined
    Recalculate with different values ↑

    FAQ

    What is tan 240°?

    tan 240° = √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 240° = √3 ≈ 1.7321.

    Why does a calculator show 2.9021 for tan 240?

    The calculator is in radian mode (RAD): it takes tan 240 as the tangent of 240 radians, tan 240 rad ≈ 2.9021. Switch it to degrees (DEG): tan 240° = √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