# Domain and Range values of cos nx,cos^(-1)nx

- Author:
- Mathguru

We can clearly see two graphs one is in red color and the second one is in green color. Red graph is the locus of the function f(x)=cos〖 (nx)〗 and green graph is the locus of the function g(x)=cos^(-1)〖 (nx)〗. We can change the value of n using the slide bar. We can also see 5 black points. These points are present on the cos x graph (red) with x-coordinates –π,-π/2,π/2,π,3π/2 . Let us change the values of n using the slide bar and see how the shape of the graphs will change. Let us change the values of n and see how the shape, domain and range of the functions cos nx & cos^(-1)nx get changed.

Questions to think about
Let us find the values of the range and domain for the function cosx.
Let us find the values of the range and domain for the function〖 cos〗^(-1)x.
Let us observe how the values of the range and domain get changed when we change the values of cos nx & cos^(-1)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 natural number?