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    Cot 15 Degrees

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

    What is cot 15°?

    Answer

    cot 15° =
    2 + √3 ≈ 3.7321

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

    ≈ — rounded to 4 decimal places.

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

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

    xyOP

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

    C(cot 15°, 1) ≈ (3.7321, 1) — where line OP meets the line y = 1; C is beyond the drawing, the arrow points to it.

    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/cot--15Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--15">Cot 15 Degrees: Cotangent of 15° on the Unit Circle</a>Copy
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    Cot 15 Degrees: Cotangent of 15° on the Unit Circle. cot 15° = 2 + √3 ≈ 3.7321. The cotangent is the ratio x/y of the point at 15° on the unit circle.
    https://calculat.io/en/number/trigonometry/cot--15/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    12°≈ 4.7046
    13°≈ 4.3315
    14°≈ 4.0108
    15°2 + √3
    16°≈ 3.4874
    17°≈ 3.2709
    18°√(5 + 2√5)
    Recalculate with different values ↑

    FAQ

    What is cot 15°?

    cot 15° = 2 + √3 ≈ 3.7321

    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 −1.1682 for cot 15?

    The calculator is in radian mode (RAD): it takes cot 15 as the cotangent of 15 radians, cot 15 rad ≈ −1.1682. Switch it to degrees (DEG): cot 15° = 2 + √3 ≈ 3.7321. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also