1. Other Types of Polar Graphs…
Sec. 6.5b

2. First, remind me of the general equation(s) of a rose curve…
Domain: All reals
Range: [–|a|, |a|]
Continuous
Symmetry: n even, symmetric about x-axis, y-axis, origin
n odd, symmetric about x-axis
n odd, symmetric about y-axis
Bounded
Maximum r-value: |a|
No asymptotes
Number of petals: n, if n is odd
2n, if n is even

3. The limacon curves are graphs of polar equations of the form
Domain: All reals
Range: [a – b, a + b]
Continuous
Symmetry: , symmetric about y-axis
, symmetric about x-axis
Bounded
Maximum r-value: a + b
No asymptotes

4. Analyze the graph of the polar curve.
Domain: All reals
Range: [0, 6]
Continuous
Symmetric about the y-axis
Bounded
Maximum r-value: 6
No asymptotes
 Support these answers with a graph???

5. Analyze the graph of the polar curve.
Domain: All reals
Range: [–1, 5]
Continuous
Symmetric about the x-axis
Bounded
Maximum r-value: 5
No asymptotes
 Support these answers with a graph???

6. Analyze the graph of the polar curve.
To graph, set 0min = – 45, 0max = 45, 0step = .1,
with viewing window [-30, 30] by [-20, 20]
Domain: All reals
Range: All reals
Continuous
Symmetric about the y-axis
Unbounded
No maximum r-value
No asymptotes

7. Analyze the graph of the polar curve.
for
Polar equations in the form
are called lemniscate curves.
Graph with a small 0step
Domain:
Range: [–2, 2]
Bounded
Continuous (on its domain)
Maximum r-value: 2
All three symmetries
No asymptotes

8. More Practice Problems
Analyze the graph of the given polar curve.
Domain: All reals
Range: [–3, 3]
Continuous
Symmetric about the x-axis, y-axis, and origin
Bounded
Maximum r-value: 3
No asymptotes

9. More Practice Problems
Analyze the graph of the given polar curve.
Domain: All reals
Range: [–1, 7]
Continuous
Symmetric about the y-axis
Bounded
Maximum r-value: 7
No asymptotes

10. More Practice Problems
Find the length of each petal of the given polar curves.
Four petals with lengths {2, 8, 2, 8}
Ten petals with lengths {7, 1, 7, 1, 7, 1, 7, 1, 7, 1}