Other Types of Polar Graphs… Sec. 6.5b

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

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

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???

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???

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

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

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

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

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}