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    Cot 75 Degrees

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

    What is cot 75°?

    Answer

    cot 75° =
    2 − √3 ≈ 0.2679

    Angle in radians: 75° = 5π/12. The point of the angle is in quadrant I, where cotangent is positive.

    ≈ — rounded to 4 decimal places.

    cot 75° = cos 75° / sin 75° = ((√6 − √2)/4) / ((√6 + √2)/4) = 2 − √3

    cot 75° = 1 / tan 75° = 1 / (2 + √3) = 2 − √3

    xyOP

    P(cos 75°, sin 75°) ≈ (0.2588, 0.9659)

    C(cot 75°, 1) ≈ (0.2679, 1) — where line OP meets the line y = 1.

    All four functions of 75°
    FunctionExact valueDecimal
    sin 75°(√6 + √2)/4≈ 0.9659
    cos 75°(√6 − √2)/4≈ 0.2588
    tan 75°2 + √3≈ 3.7321
    cot 75°2 − √3≈ 0.2679

    See Also

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    https://calculat.io/en/number/trigonometry/cot--75Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--75">Cot 75 Degrees: Cotangent of 75° on the Unit Circle</a>Copy
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    Cot 75 Degrees: Cotangent of 75° on the Unit Circle. cot 75° = 2 − √3 ≈ 0.2679. The cotangent is the ratio x/y of the point at 75° on the unit circle.
    https://calculat.io/en/number/trigonometry/cot--75/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    72°√(25 − 10√5)/5
    73°≈ 0.3057
    74°≈ 0.2867
    75°2 − √3
    76°≈ 0.2493
    77°≈ 0.2309
    78°≈ 0.2126
    Recalculate with different values ↑

    FAQ

    What is cot 75°?

    cot 75° = 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 −2.3770 for cot 75?

    The calculator is in radian mode (RAD): it takes cot 75 as the cotangent of 75 radians, cot 75 rad ≈ −2.3770. Switch it to degrees (DEG): cot 75° = 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