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    Cot 105 Degrees

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

    What is cot 105°?

    Answer

    cot 105° =
    √3 − 2 ≈ −0.2679

    Angle in radians: 105° = 7π/12. The point of the angle is in quadrant II, where cotangent is negative.

    ≈ — rounded to 4 decimal places.

    cot 105° = cot(180° − 75°) = −cot 75° = √3 − 2

    cot 105° = cos 105° / sin 105° = (−(√6 − √2)/4) / ((√6 + √2)/4) = √3 − 2

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

    xyOP

    P(cos 105°, sin 105°) ≈ (−0.2588, 0.9659)

    C(cot 105°, 1) ≈ (−0.2679, 1) — where line OP meets the line y = 1.

    All four functions of 105°
    FunctionExact valueDecimal
    sin 105°(√6 + √2)/4≈ 0.9659
    cos 105°−(√6 − √2)/4≈ −0.2588
    tan 105°−2 − √3≈ −3.7321
    cot 105°√3 − 2≈ −0.2679

    Reference angle: cot 75° = 2 − √3

    See Also

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    https://calculat.io/en/number/trigonometry/cot--105Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--105">Cot 105 Degrees: Cotangent of 105° on the Unit Circle</a>Copy
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    Cot 105 Degrees: Cotangent of 105° on the Unit Circle. cot 105° = √3 − 2 ≈ −0.2679. The cotangent is the ratio x/y of the point at 105° on the unit circle; 105° reduces to 75°.
    https://calculat.io/en/number/trigonometry/cot--105/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    98°≈ −0.1405
    100°≈ −0.1763
    101°≈ −0.1944
    105°√3 − 2
    106°≈ −0.2867
    108°−√(25 − 10√5)/5
    110°≈ −0.3640
    Recalculate with different values ↑

    FAQ

    What is cot 105°?

    cot 105° = √3 − 2 ≈ −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 0.2483 for cot 105?

    The calculator is in radian mode (RAD): it takes cot 105 as the cotangent of 105 radians, cot 105 rad ≈ 0.2483. Switch it to degrees (DEG): cot 105° = √3 − 2 ≈ −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