graphs of cot x, cot^-1 x

Author:
Mathguru
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 arccot⁡x. 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?