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    Cot 165 Degrees

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

    What is cot 165°?

    Answer

    cot 165° =
    −2 − √3 ≈ −3.7321

    Angle in radians: 165° = 11π/12. The point of the angle is in quadrant II, where cotangent is negative.

    ≈ — rounded to 4 decimal places.

    cot 165° = cot(180° − 15°) = −cot 15° = −2 − √3

    cot 165° = cos 165° / sin 165° = (−(√6 + √2)/4) / ((√6 − √2)/4) = −2 − √3

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

    xyOP

    P(cos 165°, sin 165°) ≈ (−0.9659, 0.2588)

    C(cot 165°, 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 165°
    FunctionExact valueDecimal
    sin 165°(√6 − √2)/4≈ 0.2588
    cos 165°−(√6 + √2)/4≈ −0.9659
    tan 165°√3 − 2≈ −0.2679
    cot 165°−2 − √3≈ −3.7321

    Reference angle: cot 15° = 2 + √3

    See Also

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    https://calculat.io/en/number/trigonometry/cot--165Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--165">Cot 165 Degrees: Cotangent of 165° on the Unit Circle</a>Copy
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    Cot 165 Degrees: Cotangent of 165° on the Unit Circle. cot 165° = −2 − √3 ≈ −3.7321. The cotangent is the ratio x/y of the point at 165° on the unit circle; 165° reduces to 15°.
    https://calculat.io/en/number/trigonometry/cot--165/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    160°≈ −2.7475
    162°−√(5 + 2√5)
    164°≈ −3.4874
    165°−2 − √3
    167°≈ −4.3315
    175°≈ −11.4301
    179°≈ −57.2900
    Recalculate with different values ↑

    FAQ

    What is cot 165°?

    cot 165° = −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 −0.0665 for cot 165?

    The calculator is in radian mode (RAD): it takes cot 165 as the cotangent of 165 radians, cot 165 rad ≈ −0.0665. Switch it to degrees (DEG): cot 165° = −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