Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    Tan 210 Degrees

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

    What is tan 210°?

    Answer

    tan 210° =
    √3/3 ≈ 0.5774

    Angle in radians: 210° = 7π/6. The point of the angle is in quadrant III, where tangent is positive.

    ≈ — rounded to 4 decimal places.

    tan 210° = tan(180° + 30°) = tan 30° = √3/3

    tan 210° = sin 210° / cos 210° = (−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 210°, sin 210°) ≈ (−0.8660, −0.5)

    T(1, tan 210°) ≈ (1, 0.5774) — where line OP meets the line x = 1, on the extension of the ray beyond O (dashed).

    All four functions of 210°
    FunctionExact valueDecimal
    sin 210°−1/2−0.5
    cos 210°−√3/2≈ −0.8660
    tan 210°√3/3≈ 0.5774
    cot 210°√3≈ 1.7321

    Reference angle: tan 30° = √3/3

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/trigonometry/tan--210Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--210">Tan 210 Degrees: Tangent of 210° on the Unit Circle</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    Tan 210 Degrees: Tangent of 210° on the Unit Circle. tan 210° = √3/3 ≈ 0.5774. The tangent is the ratio y/x of the point at 210° on the unit circle; 210° reduces to 30°.
    https://calculat.io/en/number/trigonometry/tan--210/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    195°2 − √3
    198°√(25 − 10√5)/5
    200°≈ 0.3640
    210°√3/3
    211°≈ 0.6009
    215°≈ 0.7002
    216°√(5 − 2√5)
    Recalculate with different values ↑

    FAQ

    What is tan 210°?

    tan 210° = √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 210° = √3/3 ≈ 0.5774.

    Why does a calculator show −0.5292 for tan 210?

    The calculator is in radian mode (RAD): it takes tan 210 as the tangent of 210 radians, tan 210 rad ≈ −0.5292. Switch it to degrees (DEG): tan 210° = √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