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# The Excel COT Function

Cotangent

The Cotangent is the reciprocal of the Tangent.

Therefore, for the simple right-angled triangle below, the cotangent of the angle θ is equal to the adjacent side, a, divided by the opposite side, o.

I.e. for the triangle above,

The trig. ratios are discussed further on the

Wikipedia Trigonometric Ratios Page

## Basic Description

The Excel Cot function calculates the cotangent of a given angle.

Note: the Cot function was only introduced in Excel 2013 and so is not available in earlier versions of Excel.

The syntax of the function is:

COT( number )

Where the number argument is the angle (in radians) that you want to calculate the cotangent of. This must be between -2^27 and +2^27.

If the supplied number argument is equal to 0, the Cot function returns the #DIV/0! error.

Converting from Degrees to Radians

If your angle is in degrees, you will need to convert it into radians before supplying it to the Cot function. This can be done using the Excel Radians function:

=RADIANS( degrees )

An example of this is given below.

## Excel Cot Function Examples

The Excel Cot Function is used in the following spreadsheet, to calculate the Cotangent of four different angles:

Formulas: | A |
---|
1 | =COT( 0.785398163397448 ) |
---|
2 | =COT( -PI() / 4 ) |
---|
3 | =COT( PI() / 2 ) |
---|
4 | =COT( RADIANS( 45 ) ) |
---|
| Results: |

Note that in the above examples:

- In cells A2 & A3, the Excel Pi function is used to supply the values -π/4 and π/2 to the function;
- In cell A4, the Excel Radians function is used to convert the angle of 45 degrees into radians before it is supplied to the Cot function.

Further details and examples of the Excel Cot function are provided on the Microsoft Office website.

## Cot Function Errors

If you get an error from the Excel Cot function, this is likely to be one of the following:

Common Errors

#DIV/0! | - | Occurs if the supplied number is equal to zero. |

#NUM! | - | Occurs if the supplied number is less than -2^27 or is greater than 2^27. |

#VALUE! | - | Occurs if the supplied number is not recognised as a numeric value. |