Question #1:
Do the calculation on the board. Include this calculation at the top of your
document. Let the two values that you get in your calculations be a1 and
a2. If a2 is 0 then you will work on the red region, if a2
is 1 you will work on the green region, if a2 is 2 you will work on the blue region.

Question #2:
Graph the equation (not filled) of
\[ r = 2+4 cos(3(\theta+\pi/8))+sin(8\theta)^2-sin(a_1 \theta)/2 \]
and show that it looks something like the graph above. You may find an extra
small loop at the origin, but try to ignore it. Graph only your region
(again, not filled) make the inner loop green and the outer loop blue.

Question #3:
Find the area of the region between the outer loop and the inner loop (only on
the region determined by a2).

Question #3:
Find the length of the outer loop and the length of the inner loop
(only on the region determined by a2).

NOTE THAT THE PENALTY FOR HANDING THIS IS LATE IS QUITE STRICT. I WANT YOU TO
DO THIS IN THE ALOTTED TIME.
You should be able to complete this quiz within the class time.
If you finish after the class time your overall grade for this assignment
will be reduced by 20% per hour (or part thereof). Make sure that your file is uploaded
by 12:30pm.
Upload your worksheet to the course
moodle.

You are expected to work alone on this assignment. Any indication of academic dishonesty
will result in a $0$ for the assignment and possible higher penalties.