Graph  and  on the same set of axes.

1. What are the values of  and ? How are they related?
2. What are the values of  and ? How are they related?
3. What are the values of  and ? How are they related?

Here is a graph of for values of between 0 and .

A graph. Horizontal axis, theta, scale 0 to 6 pi, by pi. Vertical axis, y, from negative 1 to 1, by 1s. A curve begins at 0 comma 1, crossing the x-axis at pi over 2 and ending at the point pi comma negative 1.

1. Complete the graph for values of between and .
2. Explain why your graph is correct.

Each of the graphs have been transformed from the original function . Match each graph with the transformation that was applied.