Inverse trigonometric functions

Consider the graphs of

and

below, these functions do not have the characteristics to have an inverse, why?

Sin(x) and Cos(x)

If we restrict the domain of

and

they can become 1-1 functions. Using the sliders in the graph, change the domain of

so that it becomes 1-1. You can apply the horizontal line test to check that it is 1-1. You can change the values of A and B to change the domain of

. Try reflecting

on the

line, is the resulting curve the graph of

? Apply the vertical line test to check it is.

What are the domain and target you found for

Using the sliders below, find an adequate domain so that

has an inverse. What is the target of