How do you graph r=θ?

1 Answer
Zor Shekhtman
Feb 28, 2018

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

Explanation:

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

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

Similarly, as θ increase to π, the graph intercepts X-axis at π.

Then Y-axis at 3π/2.
Then X-axis at 2π etc.

That's how a spiral form is made.

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

Related questions
See all questions in More with Polar Curves
Impact of this question
24922 views around the world
You can reuse this answer
Creative Commons License