Write your answers to these questions while clearly keeping
in mind the mantra, *"Variables vary; go slow!"*

- Jimmy said, "sin( ) has a period of 2", which means that it repeats itself whenever whatever is in the parentheses varies by 2π. So, sin(5+3
*x*) repeats itself whenever 5+3*x*varies by 2π." - What does Jimmy mean?

- Use Jimmy's insight to sketch a graph of these functions and to explain their behaviors:

*y* = cos(7*x*), -π <= *x* <= π?

*y* = cos(1/*x*),
-π <= *x* <= π?

- Use
an image of the unit circle to:
- Sketch a graph of , 0 <=
*β*<= 2π.

- Explain why the graph of , 0 <=
*β*