Problems

01

Convert points: Cartesian to Polar

Convert the Cartesian (rectangular) coordinates for these points into polar coordinates:

(a) $(\mathrm{1,0})$ $$ (b) $(3,\sqrt{3})$ $$ (c) $(-\mathrm{2,2})$ $$ (d) $(-1,\sqrt{3})$

02

Convert equations: Polar to Cartesian

Convert the polar equation to a Cartesian equation. Be sure to simplify.

(a) $r=7$ $$ (b) $r=2\sin \theta$ $$ (c) $r={\displaystyle \frac{1}{\cos \theta -\sin \theta }}$

03

Convert points: Polar to Cartesian

Convert the polar coordinates for these points into Cartesian (rectangular) coordinates:

(a) $(3,\frac{\pi }{6})$ $$ (b) $(-6,\frac{3\pi }{4})$ $$ (c) $(0,\frac{\pi }{5})$ $$ (d) $(5,-\frac{\pi }{2})$

04

Convert equations: Cartesian to Polar

Convert the Cartesian equation to a polar equation. Be sure to simplify.

(a) $x^2+y^2=25$ $$ (b) $x=5$ $$ (c) $y=x^2$

05

Sketching limaçons

Sketch the graphs of the following polar functions:

(a) $r=2+\sin \theta$ $$ (b) $r=2\cos \theta$

(c) $r=1+2\sin \theta$ $$ (d) $r=3+3\cos \theta$

06

Sketching roses

Sketch the graphs of the following polar functions. Use numbers to label the order in which the leaves/loops are traversed.

(a) $r=\sin 2\theta$ $$ (b) $r=\sin 3\theta$ $$ (c) $r=2\cos 2\theta$