Cotangent call one of trigonometrical functions - derivative of a sine and a cosine. It is odd periodic (the period is equal to Pi's number) and not continuous (gaps in points, multiple to Pi's number) function. It is possible to calculate its value in corner size, on the known lengths of the parties in a triangle, on values of a sine and cosine and other ways.
Instruction
1. If corner size is known to you, tangentit is possible to calculate value to , for example, with use of the Windows OS standard calculator. For its start open the main menu, gather from the keyboard and press Enter. Then transfer the calculator to the "engineering" mode - select item with such name in the section "Look" of the menu of the program or use a combination of the Alt keys + 2.
2. Enter corner size in degrees. The separate button for function a cotangent is not provided here therefore at first find a tangent (click on the tan button), and then divide unit into the received value (click button 1/x).
3. If the value of a tangent of the necessary corner is given in statements of the problem, for calculation of a cotangent it is not obligatory to know the size of this corner - just divide unit into the number expressing a tangent: ctg(α) = 1/tg(α). But the function tangent can define, of course, at first a-degree measure of a corner with use of the return - an arctangent, and then to calculate a cotangent of the known corner. In a general view this decision can be written down so: ctg(α) = arctg (tg(α)).
4. At the values of a sine and cosine of the necessary corner, known from conditions, there is too no need to determine its size. To find a cotangent divide the second into the first: ctg(α) = cos(α)/sin(α).
5. If in statements of the problem only one value (sine or a cosine) is provided for finding of a cotangent, transform a formula of the previous step, proceeding from sin ratio connecting them² (α) + cos² (α) = 1. From it it is possible to express one function through another: sin(α) = √ (1-cos² (α)) and cos(α) = √ (1-sin² (α)). Substitute the corresponding equality in a formula: ctg(α) = cos(α) / √ (1-cos² (α)) or ctg(α) = √ (1-sin² (α))/sin(α).
6. Without information on the size of a corner or the values of trigonometrical functions corresponding to it it is possible to calculate a cotangent in the presence of some additional data too. For example, it can be done, if the corner which cotangent needs to be calculated lies in one of tops of a rectangular triangle with the known lengths of legs. In this case calculate fraction in which numerator put length of that from legs which adjoins the necessary corner, and place length of the second in a denominator.