#1) Graph Circles with Horizontal Symmetry
var('theta')
polar_plot([cos(theta),2*cos(theta),3*cos(theta)],(theta,0,2*pi),aspect_ratio=1)
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#2) Graph Circles with Vertical Symmetry
polar_plot([sin(theta),2*sin(theta),3*sin(theta)],(theta,0,2*pi),aspect_ratio=1)
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#3) Graph Roses with Horizontal Symmetry
show(polar_plot([cos(2*theta)],(theta,0,2*pi),aspect_ratio=1))
show(polar_plot([cos(3*theta)],(theta,0,2*pi),aspect_ratio=1))
show(polar_plot([cos(4*theta)],(theta,0,2*pi),aspect_ratio=1))
show(polar_plot([cos(5*theta)],(theta,0,2*pi),aspect_ratio=1))
show(polar_plot([cos(6*theta)],(theta,0,2*pi),aspect_ratio=1))
show(polar_plot([cos(7*theta)],(theta,0,2*pi),aspect_ratio=1))
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#4) Graph Roses with Vertical Symmetry
show(polar_plot([sin(2*theta)],(theta,0,2*pi),aspect_ratio=1))
show(polar_plot([sin(3*theta)],(theta,0,2*pi),aspect_ratio=1))
show(polar_plot([sin(4*theta)],(theta,0,2*pi),aspect_ratio=1))
show(polar_plot([sin(5*theta)],(theta,0,2*pi),aspect_ratio=1))
show(polar_plot([sin(6*theta)],(theta,0,2*pi),aspect_ratio=1))
show(polar_plot([sin(7*theta)],(theta,0,2*pi),aspect_ratio=1))
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#5) Graph Cardiods with Horizontal Symmetry
show(polar_plot([2+2*cos(theta)],(theta,0,2*pi),aspect_ratio=1))
show(polar_plot([2+1*cos(theta)],(theta,0,2*pi),aspect_ratio=1))
show(polar_plot([2+3*cos(theta)],(theta,0,2*pi),aspect_ratio=1))
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#6) Graph Cardiods with Vertical Symmetry
show(polar_plot([2+2*sin(theta)],(theta,0,2*pi),aspect_ratio=1))
show(polar_plot([2+1*sin(theta)],(theta,0,2*pi),aspect_ratio=1))
show(polar_plot([2+3*sin(theta)],(theta,0,2*pi),aspect_ratio=1))
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#7) Name the conic section:
polar_plot([4/(2-cos(theta))],(theta,0,2*pi),aspect_ratio=1)
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