How do you graph r=theta?

1 Answer
Zor Shekhtman
Feb 28, 2018

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

That's how a spiral form is made.

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

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