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    Tan 30 Degrees

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

    What is tan 30°?

    Answer

    tan 30° =
    √3/3 ≈ 0.5774

    Angle in radians: 30° = π/6. The point of the angle is in quadrant I, where tangent is positive.

    ≈ — rounded to 4 decimal places.

    tan 30° = sin 30° / cos 30° = (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 30°, sin 30°) ≈ (0.8660, 0.5)

    T(1, tan 30°) ≈ (1, 0.5774) — where line OP meets the line x = 1.

    All four functions of 30°
    FunctionExact valueDecimal
    sin 30°1/20.5
    cos 30°√3/2≈ 0.8660
    tan 30°√3/3≈ 0.5774
    cot 30°√3≈ 1.7321

    See Also

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

    Tangent of nearby angles

    Angletan
    27°≈ 0.5095
    28°≈ 0.5317
    29°≈ 0.5543
    30°√3/3
    31°≈ 0.6009
    32°≈ 0.6249
    33°≈ 0.6494
    Recalculate with different values ↑

    FAQ

    What is tan 30°?

    tan 30° = √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 30° = √3/3 ≈ 0.5774.

    Why does a calculator show −6.4053 for tan 30?

    The calculator is in radian mode (RAD): it takes tan 30 as the tangent of 30 radians, tan 30 rad ≈ −6.4053. Switch it to degrees (DEG): tan 30° = √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