Polar Coordinates And Complex Numbers Worksheets With Answers - Math 611b Page 6
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50SCO: By the end of grade
Elaborations - Instructional Strategies/Suggestions
12, students will be
Graphs of Polar Equations (9.2)
expected to:
The classical curves using polar coordinates are described in the table on
C97 construct and examine
p.564. There are three major categories:
graphs in the polar
plane
< rose - of which a lemniscate is a special case.
< limacon - of which a cardioid is a special case.
< spiral
Example: Graph r = 2 cos 3 2 .
The general equation for a rose is r = a cos n 2 ;
where n is even, then there are 2n petals
where n is odd, then there is n petals
General Equations:
< rose - r = a cos n 2 or r = a sin n 2
cos 2 2 or r = a
sin 2 2
< lemniscate of Bernoulli- r
2
2
2
= a
< limacon of Pascal - r = a + b cos 2 or r = a + b sin 2
< cardioid - r = a + a cos 2 or r = a + a sin 2
< spiral of Archimedes - r = a 2 ( 2 must be in radians)
Extension:
< Cissoid of Diocles - r = 2a tan 2 sin 2
6
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