|A right triangle.
A long time ago, three important trigonometric ratios were committed to memory thanks to the mnemonic SOH-CAH-TOA. These ratios are the sine, cosine, and tangent.
|The "versed sine" or "versine".
|The reciprocal trigonometric functions.
Which brings me to the Canadian structural concrete design standard, CSA A23.3. The folks who wrote CSA A23.3 seem to have a special place in their hearts for the cotangent. While it is certainly well within their rights to be especially fond of any mathematical function of their choosing, I don't understand why a design standard, written by engineers for engineers, would put a useless trigonometric function in a math expression. When I see a cotangent, I see unnecessary extra work. My calculator doesn't come equipped with a 'cot' button, but I do have 'sin', 'cos', and 'tan' buttons. Where there's a cotangent, I have to take a moment (however brief) to recall that the cotangent is really just the reciprocal of the tangent. I then have to rearrange the formula using the tangent in order to punch the right buttons on the calculator to get my answer.
Sure, this is only a tiny amount of extra work, even if I forget the cotangent's definition and have to do a quick internet search. But why not make the code's expression a little more practical? Save the user's time and effort by expressing formulas the way they are actually used: the way they're entered into a calculator.