Assignment #11

Question #1:
Graph the following polar equation. \[ r = 1-3cos(\theta)sin(2\theta)+2sin^2(\theta)+cos(16\theta) \] Find a numeric estimate of the area of the region inside the graph of the polar plot but subtract off the area that is inside regions which are completely inside other regions. On a separate graph, show just the parts of the plot which make small loops near the origin (everything except the two big loops).

Question #2:
Graph the following polar curve and show that it cuts out 5 different regions. Find the area of each of those regions. \[ r = 1+6sin(\theta)+cos(6\theta)\] Draw the unfolded polar plot where the regions don't overlap.
Find the arc length (numeric value) for each of the loops of this (the unfolded) graph. Recall from your calculus class that formula for the arc length is equal to \[ \int_{\theta_1}^{\theta_2} \sqrt{ r(\theta)^2 + r'(\theta)^2 } d\theta~. \]

You should open up a new worksheet and start from scratch. You will have to save your work in a file and upload that file on to the course moodle. Your solution should be a sequence of commands where it is easy to change the input string and after you execute the sequence of commands you should have the correct output string. Please add documentation to your worksheet to explain how it works. Just a few sentences is sufficient, but imagine that you were opening up the worksheet for the first time and wanted to know what it did. You will be marked down if what you write is not clear and coherent.

You should finish your assignment by Wednesday, November 21 by 11:59pm. Assignments submitted after this date will be assessed a penalty of 10% per day.