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?
Inverse of sin(x)
What is the restricted range you found for ? Which two quadrants from the Unit Circle do these values correspond to?
Inverse of cos(x)
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?