graphs of cot x, cot^-1 x
You can clearly see two graphs one is in red color and second one is in green color.Red graph is the locus of the function f(x)=cot〖 (nx)〗 and green graph is the locus of the function g(x)=cot^(-1)〖 (nx)〗. you can change the value of n ucotg slide bar. You can also see 10 black points. These points are present on the cot x graph (red) with x-coordinates- 5π/2,-2π,-3π/2,–π,-π/2,π/2,π,3π/2,5π/2,2π . Change the values of n ucotg slide bar and see how the shape of the graphs will change.
Questions to think about Find the range and domain of the function〖 cot〗x. Find the range and domain of the function arccotx. Let us observe how the range and domain get changed when we change the values of cot nx and arccot nx. Let us change the value of n and observe at which value along the x- axis we get the maximum and minimum values of the graph. What happens when n is a natural number?