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    Tan 15 Degrees

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

    What is tan 15°?

    Answer

    tan 15° =
    2 − √3 ≈ 0.2679

    Angle in radians: 15° = π/12. The point of the angle is in quadrant I, where tangent is positive.

    ≈ — rounded to 4 decimal places.

    tan 15° = sin 15° / cos 15° = ((√6 − √2)/4) / ((√6 + √2)/4) = 2 − √3

    tan 15° = tan(45° − 30°) = (1 − √3/3) / (1 + √3/3) = 2 − √3

    xyOP

    P(cos 15°, sin 15°) ≈ (0.9659, 0.2588)

    T(1, tan 15°) ≈ (1, 0.2679) — where line OP meets the line x = 1.

    All four functions of 15°
    FunctionExact valueDecimal
    sin 15°(√6 − √2)/4≈ 0.2588
    cos 15°(√6 + √2)/4≈ 0.9659
    tan 15°2 − √3≈ 0.2679
    cot 15°2 + √3≈ 3.7321

    See Also

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    https://calculat.io/en/number/trigonometry/tan--15Copy
    <a href="https://calculat.io/en/number/trigonometry/tan--15">Tan 15 Degrees: Tangent of 15° on the Unit Circle</a>Copy
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    Tan 15 Degrees: Tangent of 15° on the Unit Circle. tan 15° = 2 − √3 ≈ 0.2679. The tangent is the ratio y/x of the point at 15° on the unit circle.
    https://calculat.io/en/number/trigonometry/tan--15/generated.jpgCopy

    Tangent of nearby angles

    Angletan
    12°≈ 0.2126
    13°≈ 0.2309
    14°≈ 0.2493
    15°2 − √3
    16°≈ 0.2867
    17°≈ 0.3057
    18°√(25 − 10√5)/5
    Recalculate with different values ↑

    FAQ

    What is tan 15°?

    tan 15° = 2 − √3 ≈ 0.2679

    How are sin 15° and cos 75° related?

    They are equal: sin α = cos(90° − α), and 15° + 75° = 90°. So sin 15° = cos 75° = (√6 − √2)/4, cos 15° = sin 75° = (√6 + √2)/4, and tan 15° = cot 75° = 2 − √3.

    Why does a calculator show −0.8560 for tan 15?

    The calculator is in radian mode (RAD): it takes tan 15 as the tangent of 15 radians, tan 15 rad ≈ −0.8560. Switch it to degrees (DEG): tan 15° = 2 − √3 ≈ 0.2679. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also