Consider the graphs of [math]sin(x)[/math], [math]cos(x)[/math] and [math]tan(x)[/math] below. These functions do not have the characteristics to have an inverse that is also a function. Why?

If we restrict the domain of [math]sin(x)[/math] and [math]cos(x)[/math] they can become 1-1 functions. Using the sliders in the graph, change the domain of [math]sin(x)[/math] so that it becomes 1-1. You can apply the horizontal line test to check that it is 1-1.[br][br]You can change the values of A and B to change the domain of [math]sin(x)[/math]. Try reflecting [math]sin(x)[/math] on the [math]y=x[/math] line, is the resulting curve the graph of [math]arcsin(x)[/math]? Apply the vertical line test to check it is. [br][br]How does this change the range of the inverse graphs?

What is the restricted range you found for [math]arcsin(x)[/math]?[br][br]Which two quadrants from the Unit Circle do these values correspond to?

[br]Using the sliders below, find an adequate domain so that [math]cos(x)[/math] has an inverse that is a function. What is the new restricted range of [math]arccos(x)[/math]? Which two quadrants from the Unit Circles do these values correspond to?