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    Cot 126 Degrees

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

    What is cot 126°?

    Answer

    cot 126° =
    −√(5 − 2√5) ≈ −0.7265

    Angle in radians: 126° = 7π/10. The point of the angle is in quadrant II, where cotangent is negative.

    ≈ — rounded to 4 decimal places.

    cot 126° = cot(180° − 54°) = −cot 54° = −√(5 − 2√5)

    cot 126° = cos 126° / sin 126° = (−√(10 − 2√5)/4) / ((√5 + 1)/4) = −√(5 − 2√5)

    Regular pentagon (golden ratio): cos 36° = (√5 + 1)/4.

    cot 54° = tan 36° = sin 36° / cos 36° = √(5 − 2√5)

    xyOP

    P(cos 126°, sin 126°) ≈ (−0.5878, 0.8090)

    C(cot 126°, 1) ≈ (−0.7265, 1) — where line OP meets the line y = 1.

    All four functions of 126°
    FunctionExact valueDecimal
    sin 126°(√5 + 1)/4≈ 0.8090
    cos 126°−√(10 − 2√5)/4≈ −0.5878
    tan 126°−√(25 + 10√5)/5≈ −1.3764
    cot 126°−√(5 − 2√5)≈ −0.7265

    Reference angle: cot 54° = √(5 − 2√5)

    See Also

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    https://calculat.io/en/number/trigonometry/cot--126Copy
    <a href="https://calculat.io/en/number/trigonometry/cot--126">Cot 126 Degrees: Cotangent of 126° on the Unit Circle</a>Copy
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    Cot 126 Degrees: Cotangent of 126° on the Unit Circle. cot 126° = −√(5 − 2√5) ≈ −0.7265. The cotangent is the ratio x/y of the point at 126° on the unit circle; 126° reduces to 54°.
    https://calculat.io/en/number/trigonometry/cot--126/generated.jpgCopy

    Cotangent of nearby angles

    Anglecot
    110°≈ −0.3640
    120°−√3/3
    125°≈ −0.7002
    126°−√(5 − 2√5)
    127°≈ −0.7536
    130°≈ −0.8391
    134°≈ −0.9657
    Recalculate with different values ↑

    FAQ

    What is cot 126°?

    cot 126° = −√(5 − 2√5) ≈ −0.7265

    How are sin 36° and cos 54° related?

    They are equal: sin α = cos(90° − α), and 36° + 54° = 90°. So sin 36° = cos 54° = √(10 − 2√5)/4, cos 36° = sin 54° = (√5 + 1)/4, and tan 36° = cot 54° = √(5 − 2√5).

    Why does a calculator show 2.8606 for cot 126?

    The calculator is in radian mode (RAD): it takes cot 126 as the cotangent of 126 radians, cot 126 rad ≈ 2.8606. Switch it to degrees (DEG): cot 126° = −√(5 − 2√5) ≈ −0.7265. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

    See Also