8.4 Polar coordinates: graphs  (Page 7/16)

Describe the three types of symmetry in polar graphs, and compare them to the symmetry of the Cartesian plane.

Which of the three types of symmetries for polar graphs correspond to the symmetries with respect to the x -axis, y -axis, and origin?

What are the steps to follow when graphing polar equations?

Describe the shapes of the graphs of cardioids, limaçons, and lemniscates.

What part of the equation determines the shape of the graph of a polar equation?

$r=5\cos 3\theta$

$r=3-3\cos \theta$

$r=3+2\sin \theta$

$r=3\sin 2\theta$

$r=4$

$r=2\theta$

$r=4\cos \frac{\theta }{2}$

$r=\frac{2}{\theta }$

$r=3\sqrt{1-{\cos }^2\theta }$

$r=\sqrt{5\sin 2\theta }$

$r=3\cos \theta$

$r=4\sin \theta$

$r=2+2\cos \theta$

$r=2-2\cos \theta$

$r=5-5\sin \theta$

$r=3+3\sin \theta$

$r=3+2\sin \theta$

$r=7+4\sin \theta$

$r=4+3\cos \theta$

$r=5+4\cos \theta$

$r=10+9\cos \theta$

$r=1+3\sin \theta$

$r=2+5\sin \theta$

$r=5+7\sin \theta$

$r=2+4\cos \theta$

$r=5+6\cos \theta$

$r^2=36\cos \left(2\theta \right)$

$r^2=10\cos \left(2\theta \right)$

$r^2=4\sin \left(2\theta \right)$

$r^2=10\sin \left(2\theta \right)$

$r=3\text{sin}(2\theta )$

$r=3\text{cos}(2\theta )$

$r=5\text{sin}(3\theta )$

$r=4\text{sin}(4\theta )$

$r=4\text{sin}(5\theta )$

$r=-\theta$

$r=2\theta$

$r=-3\theta$

$r=\frac{1}{\theta }$

$r=\frac{1}{\sqrt{\theta }}$

$r=2\sin \theta \tan \theta ,$ a cissoid

$r=2\sqrt{1-{\sin }^2\theta }$ , a hippopede

$r=5+\cos \left(4\theta \right)$

$r=2-\sin \left(2\theta \right)$

$r={\theta }^2$

$r=\theta +1$

$r=\theta \sin \theta$

$r=\theta \cos \theta$

$r=\theta ,r=-\theta$

$r=\theta ,r=\theta +\sin \theta$

$r=\sin \theta +\theta ,r=\sin \theta -\theta$

$r=2\sin \left(\frac{\theta }{2}\right),r=\theta \sin \left(\frac{\theta }{2}\right)$

$r=\sin \left(\cos (3\theta )\right)r=\sin (3\theta )$

On a graphing utility, graph $r=\sin \left(\frac{16}{5}\theta \right)$ on $\left[0,4\pi \right],\left[0,8\pi \right],\left[0,12\pi \right],$ and $\left[0,16\pi \right].$ Describe the effect of increasing the width of the domain.

On a graphing utility, graph and sketch $r=\sin \theta +{\left(\sin \left(\frac{5}{2}\theta \right)\right)}^3$ on $\left[0,4\pi \right].$

On a graphing utility, graph each polar equation. Explain the similarities and differences you observe in the graphs.

On a graphing utility, graph each polar equation. Explain the similarities and differences you observe in the graphs.

On a graphing utility, graph each polar equation. Explain the similarities and differences you observe in the graphs.

$r_1=3+2\sin \theta ,r_2=2$

$r_1=6-4\cos \theta ,r_2=4$

$r_1=1+\sin \theta ,r_2=3\sin \theta$

$r_1=1+\cos \theta ,r_2=3\cos \theta$

$r_1=\cos \left(2\theta \right),r_2=\sin \left(2\theta \right)$

$r_1={\sin }^2\left(2\theta \right),r_2=1-\cos \left(4\theta \right)$

$r_1=\sqrt{3},r_2=2\sin \left(\theta \right)$

$r_1{}^2=\sin \theta ,r_2{}^2=\cos \theta$

$r_1=1+\cos \theta ,r_2=1-\sin \theta$