# How do you graph basic polar equations?

Dec 28, 2014

You consider a function of the type:
$r = f \left(\theta\right)$

So you give values of the angle $\theta$ and the function gives you values of $r$.

To graph polar functions you have to find points that lie at a distance $r$ from the origin and form (the segment $r$) an angle $\theta$ with the $x$ axis.

Take for example the polar function:
$r = 3$

This function describes points that for every angle $\theta$ lie at a distance of 3 from the origin!!!

Graphically:

The result is a circle of radius $r = 3$.

Now, the only complication is when $r$ becomes NEGATIVE ...how do I plot this?
We use a trick....we take the positive and flip it about the origin!!!!!!

Take for example the polar function:
$r = - 3$

This function describes points that for every angle $\theta$ lie at a distance of...-3 from the origin????
We use our trick!

Graphically:

Every point of the old graph flipped about the origin!!!!
It is a circle...again!!!!

Now try by yourself with:
$r = 2 \cos \left(\theta\right)$
Build a table of $\theta$ and $r$ and plot it...you should get another circle but with its center....on the $x$ axis (in $\left(1 , 0\right)$) and radius =1.

There are more complicated (and graphically beautiful) polar functions such as limacons, cardioids, roses, lemniscates, etc…try them!!!