PrecisionCalc
xl
Precision
Get Your Numbers Right
xlpCOS
Returns the cosine of an angle, with up to 32,767 significant digits of precision. Same as Excel's built-in COS function, but with high precision.
For any given angle in a right triangle, the angle's cosine is the length of the side between the angle and the right angle (the "adjacent" side), divided by the length of the side opposite the right angle (the "hypotenuse").
Syntax
xlpCOS(num,maximum_significant_digits)
num | Required. The angle, in radians, for which to find the cosine. |
maximum_significant_digits | Optional. Determines the maximum number of significant digits to be returned. Default is the maximum number allowed by the edition of xlPrecision. |
Remarks
num must be in radians, not degrees. To find the cosine of an angle given in degrees, first convert the degrees to radians with xlpRADIANS (or Pi/180).
xlPrecision results are returned as text that look like numbers, not as values that Excel recognizes as numbers. This is because Excel would truncate the results to 15 significant digits if it recognized them as numbers.
num can accept both numbers and text.
num can accept text up to 32,767 characters long.
maximum_significant_digits is ignored if it is higher than the maximum significant digits allowed by the edition of xlPrecision.
Use maximum_significant_digits to increase calculation speed where desired. The lower the number used, the faster the calculation.
You can use the results of xlPrecision functions as the operands in other xlPrecision formulas without losing any precision, but using them as operands in Excel's arithmetic functions will truncate them to 15 significant digits.
If the return value is so large that it has more than 32,767 characters to the left of the decimal, then xlPrecision is of course unable to return a correct value and instead returns "#VALUE!". Note, that's a vastly larger number than Excel can return without xlPrecision. Excel itself can only return or recognize a number with no more than 308 digits to the left of the decimal.
The 32,767 SD edition can only provide a maximum of 32,767 total characters, including all formatting characters such as decimal, leading hyphen or parentheses for negatives, and thousands separators. As a result, it can only return the maximum 32,767 significant digits when the result is an unformatted positive integer. This is due to Excel's limitation of 32,767 characters in a cell. In all cases, the 32,767 SD edition will give you as many significant digits as possible with the formatting you have chosen.
Depending on how many significant digits the edition of xlPrecision provides, the result may be too long to conveniently view. You can view the full result by right-clicking the cell and choosing Format Cells | Alignment | Wrap Text, and widening the column to the width of the screen. An easy way to view the full result without changing column widths or wrapping text is to right-click the cell, choose Copy, and then paste into Notepad or a word processor.
Examples
Formula | Description |
=xlpCOS(0.25) | Cosine of angle of 0.25 radians. |
=xlpCOS(xlpRADIANS(15)) | Cosine of angle of 15 degrees. |
See Also