Inverse trigonometric functions

Consider the graphs of

and

below. These functions do not have the characteristics to have an inverse that is also a function. 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. How does this change the range of the inverse graphs?

What is the restricted range you found for

? Which two quadrants from the Unit Circle do these values correspond to?

Using the sliders below, find an adequate domain so that

has an inverse that is a function. What is the new restricted range of

? Which two quadrants from the Unit Circles do these values correspond to?