Question

How do you graph `r=theta`?

Answer 1

The graph is a spiral that starts from the origin of coordinates (when `theta`=0) and unravels counterclockwise.

Explanation:

As `theta` increases from 0 to `pi`/2, the graph moves from the the origin of coordinates counterclockwise, getting farther and farther from it.

It intercepts the Y-axis at point `pi`/2 because, when `theta`=`pi`/2, r=`pi`/2.
Therefore, x=rcos(`theta`)=(`pi`/2)cos(`pi`/2)=0 and y=rsin(`theta`)=(`pi`/2)sin(`pi`/2)=`pi`/2.

Similarly, as `theta` increase to `pi`, the graph intercepts X-axis at `pi`.

Then Y-axis at 3`pi`/2.
Then X-axis at 2`pi` etc.

That's how a spiral form is made.

Do a Google search for "r=theta graph" to see how the graph looks.