Polar Coordinates And Complex Numbers Worksheets With Answers - Math 611b Page 9
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50Polar Equation Worksheet (9.2) Part 2
1. Write a polar equation whose graph is a rose.
2. Determine the maximum value of r in the equation r = 3 + 5 sin 2 . What is the minimum value of r?
3. Identify the type of curve each represents, then graph.
a) r = 1 + sin 2
b) 2 ! 3 sin 2
c) r = cos 2 2
d) r = 1.5 2
e) r = ! 3 sin 2
f) r = 3 + 3 cos 2
g)r = 3 2
= 4 cos 2 2
i) r = 2 sin 3 2
2
h) r
j) r = ! 2 sin 3 2
k) r = 5 2 /2
l) r = ! 5 + 3 cos 2
m) r = ! 2 ! 2 sin 2
= 9 sin 2 2
o) r = 9 sin 2 2
2
n) r
p) r = sin 4 2
q) r = 2 + 2 cos 2
4. Graph each system of polar equations. Solve the system using algebra and trigonometry. Assume
#
2 < 2 B .
0
b) r = 1 + cos 2
c) r = 2 sin 2
a) r = 3
r = 2 + cos 2
r = 1 ! cos 2
r = 2 sin 2 2
5. Graph each system using a graphing calculator. Find the points of intersection. Round coordinates to
#
2 < 2 B .
the nearest tenth. Assume 0
b) r = 3 + 3 sin 2
c) r = 2 + 2 cos 2
a) r = 1
r = 2 cos 2 2
r = 3 + sin 2
r = 2
9
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