Creating Inverse Sine and Inverse Cosine Functions
Interact with this app for a few minutes. Then answer the questions that follow.
Why is the graph of y = sin(x) a function? Explain. Be sure to use the terms "input" and "output" in your explanation.
Move the xMin point to and move the xMax point to . The equation of the inverse relation with dashed graph is . Is this dashed graph a function? Explain why or why not. Make sure to use the terms "input" and "output" in your explanation.
For the function y = sin(x), move the xMin and xMax to restrict the domain of this original function. Is it possible to restrict the domain so the inverse relation (with dashed graph) becomes a function? If so, show how this can be done and state this restricted domain below. If not, clearly explain why this is impossible.
Interact with this app for a few minutes. Then answer the questions that follow.
Why is the graph of y = cos(x) a function? Explain. Be sure to use the terms "input" and "output" in your explanation.
Move the xMin point to and move the xMax point to . The equation of the inverse relation with dashed graph is . Is this dashed graph a function? Explain why or why not. Make sure to use the terms "input" and "output" in your explanation.
For the function y = cos(x), move the xMin and xMax to restrict the domain of this original function. Is it possible to restrict the domain so the inverse relation (with dashed graph) becomes a function? If so, show how this can be done and state this restricted domain below. If not, clearly explain why this is impossible.