Question

How do you graph basic polar equations?

Answer 1

You consider a function of the type:
`r=f(theta)`

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=2cos(theta)`
Build a table of `theta` and `r` and plot it...you should get another circle but with its center....on the `x` axis (in `(1,0)`) and radius =1.

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