Documentation/Calc Functions/COT

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    Function name:

    COT

    Category:

    Mathematical

    Summary:

    Calculates the trigonometric cotangent (cot) of an angle expressed in radians.

    Syntax:

    COT(Number)

    Returns:

    Returns a real number that is the trigonometric cotangent of the specified angle.

    Arguments:

    Number is a real number, or a reference to a cell containing that number, which is the angle in radians whose trigonometric cotangent is to be calculated.

    • If Number is non-numeric, then COT reports a #VALUE! error.
    • If Number is equal to 0, then COT reports a #NUM! error.

    Additional details:

    If your angle is expressed in degrees, either multiply by PI()/180 or use the RADIANS function to convert to radians.

    The formula for the trigonometric cotangent of x is:

    [math]\displaystyle{ \cot (x)~=~ \frac{1}{\tan(x)} ~=~\frac{\cos(x)}{\sin(x)} }[/math]

    Mathematically, the cotangent of any integer multiple of π, i.e. {......-2π, -π, 0, π, 2π.....} is undefined. For this reason, COT reports an error when its argument is equal to 0. However, because of the inherent inaccuracy in representing π numerically, COT does not report errors for other argument values. You should be aware that COT will return large positive or negative results for non-zero integer values of π.

    The figure below illustrates the function COT.

    COT function

    Examples:

    Formula Description Returns
    =COT(1) Trigonometric cotangent of 1 radian. 0.642092615934331
    =COT(D1) where cell D1 contains the number -0.5. Trigonometric cotangent of -½ radian. −1.83048772171245
    =COT(PI()/4) Trigonometric cotangent of π/4 radians. 1
    =COT(RADIANS(60)) Trigonometric cotangent of 60°, after first converting the angle from degrees to radians. 0.577350269189626
    =DEGREES(ACOT(COT(RADIANS(60))) An angle of 60° is converted to radians, its cotangent is taken, then the inverse cotangent of that value is calculated, and finally the result is converted back to degrees. 60

    Related LibreOffice functions:

    ACOT

    COS

    CSC

    SEC

    SIN

    TAN

    ODF standard:

    Section 6.16.21, part 2

    Related (or similar) Excel functions:

    COT since v.2013.