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

Author:
Mathguru
We 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)=sin⁡〖 (nx)〗 and the green graph is the locus of the function g(x)=sin^(-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 sin 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 sin nx,sin^(-1) nx get changed
Questions to think about Find the range and domain of the function〖 sin〗⁡x. Find the range and domain of the function sin^(-1)⁡x. Let us observe how the range and domain get changed when we change the values of sin nx and sin^(-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 a natural number?