Polar Coordinates And Complex Numbers Worksheets With Answers - Math 611b Page 8
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50Polar Equation Worksheet (9.2) Part 1
1. Graph the following classical curves. Inductively state the pattern that evolves.
a) r = cos 2
b) r = 2 cos 2
c) r = 3 cos 2
d) What effect does “a” have on the graph?
e) Make a conjecture as to how the r = sin 2 graph compares with the r = cos 2 graph.
2. Verify your conjecture by graphing the following:
a) r = sin 2
b) r = 2 sin 2
c) r = 3 sin 2
3. Graph the following classical curves. Inductively state the pattern that evolves.
a) r = 2 cos 2
b) r = 2 cos 2 2
c) r = 2 cos 3 2
d) What effect does “n” have on the graph?
e) Make a prognostication as to what r = 2 cos 5 2 would look like. Verify your prognostication by
graphing.
4. Graph the following classical curves. Inductively state the pattern that evolves.
a) r = 1 + 2 cos 2
b) r = 2 + 2 cos 2
c) r = 3 + 2 cos 2
d) r = 4 + 2 cos 2
e) What effect does “a” have on the graph?
f) Which of these curves is a cardioid?
g) Predict what the graph of r = 1 + 2 sin 2 would look like. Verify your prediction by graphing.
h) Take part (c) above and investigate what effect changing the sign of “a” and/or “b” has on the basic
graph. Check your work by trying a few more examples. Finally make a statement about the effects of
the size and sign of these coefficients on the graph and convey this to the class.
5. Graph the following classical curves:
= 4 cos 2 2
2
a) r
= 4 sin 2 2
2
b) r
c) What is the name for this particular classical curve?
6. Graph the following classical curves. Inductively state the pattern that evolves
a) r = 2
b) r = 2 2
c) r = 3 2
d) r = !2
e) r = ! 2 2
f) r = ! 3 2
g) What effect does the “a” coefficient have on the graph?
8
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