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 cos⁡x. 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?