4.3 Polar coordinates  (Page 5/8)

How are the polar axes different from the x - and y -axes of the Cartesian plane?

Explain how polar coordinates are graphed.

How are the points $\left(3,\frac{\pi }{2}\right)$ and $\left(-3,\frac{\pi }{2}\right)$ related?

Explain why the points $\left(-3,\frac{\pi }{2}\right)$ and $\left(3,-\frac{\pi }{2}\right)$ are the same.

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

$\left(5,\pi \right)$

$\left(6,-\frac{\pi }{4}\right)$

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

$\left(4,\frac{7\pi }{4}\right)$

$\left(4,2\right)$

$\left(-4,6\right)$

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

$\left(\mathrm{-10},\mathrm{-13}\right)$

$\left(8,8\right)$

$x=3$

$y=4$

$y=4x^2$

$y=2x^4$

$x^2+y^2=4y$

$x^2+y^2=3x$

$x^2-y^2=x$

$x^2-y^2=3y$

$x^2+y^2=9$

$x^2=9y$

$y^2=9x$

$9xy=1$

$r=3\sin \theta$

$r=4\cos \theta$

$r=\frac{4}{\sin \theta +7\cos \theta }$

$r=\frac{6}{\cos \theta +3\sin \theta }$

$r=2\sec \theta$

$r=3\csc \theta$

$r=\sqrt{r\cos \theta +2}$

$r^2=4\sec \theta \csc \theta$

$r=4$

$r^2=4$

$r=\frac{1}{4\cos \theta -3\sin \theta }$

$r=\frac{3}{\cos \theta -5\sin \theta }$

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

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

$\left(3.5,\frac{7\pi }{4}\right)$

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

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

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

$\left(3,\frac{5\pi }{6}\right)$

$\left(-1.5,\frac{7\pi }{6}\right)$

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

$\left(1,\frac{3\pi }{2}\right)$

$5x-y=6$

$2x+7y=-3$

$x^2+{\left(y-1\right)}^2=1$

${\left(x+2\right)}^2+{\left(y+3\right)}^2=13$

$x=2$

$x^2+y^2=5y$

$x^2+y^2=3x$

$r=6$

$r=-4$

$\theta =-\frac{2\pi }{3}$

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

$r=\sec \theta$

$r=\mathrm{-10}\sin \theta$

$r=3\cos \theta$

Use a graphing calculator to find the rectangular coordinates of $\left(2,-\frac{\pi }{5}\right).$ Round to the nearest thousandth.

Use a graphing calculator to find the rectangular coordinates of $\left(-3,\frac{3\pi }{7}\right).$ Round to the nearest thousandth.

Use a graphing calculator to find the polar coordinates of $\left(-7,8\right)$ in degrees. Round to the nearest thousandth.

Use a graphing calculator to find the polar coordinates of $\left(3,-4\right)$ in degrees. Round to the nearest hundredth.

Use a graphing calculator to find the polar coordinates of $\left(-2,0\right)$ in radians. Round to the nearest hundredth.

Describe the graph of $r=a\sec \theta ;a>0.$

Describe the graph of $r=a\sec \theta ;a<0.$

Describe the graph of $r=a\csc \theta ;a>0.$

Describe the graph of $r=a\csc \theta ;a<0.$

What polar equations will give an oblique line?

$r<4$

$0\le \theta \le \frac{\pi }{4}$

$\theta =\frac{\pi }{4},r\ge 2$

$\theta =\frac{\pi }{4},r\ge \mathrm{-3}$

$0\le \theta \le \frac{\pi }{3},r<2$

$\frac{-\pi }{6}<\theta \le \frac{\pi }{3},-3<r<2$