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+3x) repeats itself whenever
5+3x 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(7x), -π <= x <= π?
y = cos(1/x),
-π <= x <= π?
an image of the unit circle to:
- Sketch a graph of , 0 <= β <= 2π.
- Explain why the graph of , 0 <= β
<= 2π, behaves as it does.