7.3 Polar coordinates  (Page 6/16)

$\left(3,\frac{\pi }{6}\right)$

$\left(\mathrm{-2},\frac{5\pi }{3}\right)$

$\left(0,\frac{7\pi }{6}\right)$

$\left(\mathrm{-4},\frac{3\pi }{4}\right)$

$\left(1,\frac{\pi }{4}\right)$

$\left(2,\frac{5\pi }{6}\right)$

$\left(1,\frac{\pi }{2}\right)$

Coordinates of point A .

Coordinates of point B .

Coordinates of point C .

Coordinates of point D .

$\left(2,2\right)$

$\left(3,\mathrm{-4}\right)$ (3, −4)

$\left(8,15\right)$

$\left(\mathrm{-6},8\right)$

$\left(4,3\right)$

$\left(3,\text{−}\sqrt{3}\right)$

$\left(2,\frac{5\pi }{4}\right)$

$\left(\mathrm{-2},\frac{\pi }{6}\right)$

$\left(5,\frac{\pi }{3}\right)$

$\left(1,\frac{7\pi }{6}\right)$

$\left(\mathrm{-3},\frac{3\pi }{4}\right)$

$\left(0,\frac{\pi }{2}\right)$

$\left(\mathrm{-4.5},6.5\right)$

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

$r^2=9\text{cos}\theta$

$r=\text{cos}\left(\frac{\theta }{5}\right)$

$r=2\text{sec}\theta$

$r=1+\text{cos}\theta$

$r=3$

$\theta =\frac{\pi }{4}$

$r=\text{sec}\theta$

$r=\text{csc}\theta$

$x^2+y^2=16$

$x^2-y^2=16$

$x=8$

$3x-y=2$

$y^2=4x$

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

$r=6\text{cos}\theta$

$r=\theta$

$r=\text{cot}\theta \text{csc}\theta$

$r=1+\text{sin}\theta$

$r=3-2\text{cos}\theta$

$r=2-2\text{sin}\theta$

$r=5-4\text{sin}\theta$

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

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

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

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

$r^2=4\text{cos}\left(2\theta \right)$

$r^2=4\text{sin}\theta$

$r=2\theta$

[T] The graph of $r=2\text{cos}(2\theta )\text{sec}(\theta ).$ is called a strophoid. Use a graphing utility to sketch the graph, and, from the graph, determine the asymptote.

[T] Use a graphing utility and sketch the graph of $r=\frac{6}{2\text{sin}\theta -3\text{cos}\theta }.$

[T] Use a graphing utility to graph $r=\frac{1}{1-\text{cos}\theta }.$

[T] Use technology to graph $r=e^{\text{sin}(\theta )}-2\text{cos}\left(4\theta \right).$

[T] Use technology to plot $r=\text{sin}\left(\frac{3\theta }{7}\right)$ (use the interval $0\le \theta \le 14\pi ).$

Without using technology, sketch the polar curve $\theta =\frac{2\pi }{3}.$

[T] Use a graphing utility to plot $r=\theta \text{sin}\theta$ for $\text{−}\pi \le \theta \le \pi .$

[T] Use technology to plot $r=e^{\mathrm{-0.1}\theta }$ for $\mathrm{-10}\le \theta \le 10.$

[T] There is a curve known as the “ Black Hole .” Use technology to plot $r=e^{\mathrm{-0.01}\theta }$ for $\mathrm{-100}\le \theta \le 100.$

[T] Use the results of the preceding two problems to explore the graphs of $r=e^{\mathrm{-0.001}\theta }$ and $r=e^{\mathrm{-0.0001}\theta }$ for $\left|\theta \right|>100.$