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, 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.

What are the domain and target you found for [math]arcsin(x)[/math]?

[br]Using the sliders below, find an adequate domain so that [math]cos(x)[/math] has an inverse. What is the target of [math]arccos(x)[/math]?