Do all of these
problems in polar coordinates. To graph in polar coordinates in GC, type *r=*some expession involving theta. (Type "theta" to actually see the symbol "θ".)

1. Explain
how to graph the function *f*(*θ*) = in polar coordinates, where 0 <= θ <= 2π.
Then draw the graph.

2. GC
continues to show the x-y coordinate plane even when you are graphing in polar
coordinates. Does this matter? If so, how? If not, why?

3. Enter
the function *r* = sin(*θ*). The graph appears to be a circle. How
can you tell for sure?

4. The
graph of *r* = sin(*θ*) in polar coordinates is a circle of
diameter 1 centered at *x*=0,
*y*=0.5. Is it possible
for a function to have a circle of diameter 2 centered at *x*=0,*y*=0.5 as its graph in polar coordinates? Explain.

5. Enter
the function y = cos(2*θ*), 0 <= *θ* <= 2π. Now do this: Construct the graph in polar coordinates
by hand, with paper and pencil, using a ruler and a calculator.

Explain
why the graph of *y* = cos(2*θ*) seems to "loop" four times. *(Relate
the behavior of *cos(2*θ*)* in polar coordinates to the behavior
of *cos(2*x*)* in rectangular coordinates, where
both *__θ__* and x vary from 0 to 2π radians. If you really understand your explanation, then you should also be able to explain why the graph of cos(3*

Use this GC graph to investigate your functions and see them traced as

6. Make up a neat graph of your own to share next Monday. Why do you consider it a "neat graph"?

7. Try
to make these graphs (these are all made with 0 <= *θ* <= 2π).

8. Use
what you learned about why behaves as it does to explain why the
graph of behaves as it
does.