Answer
This is a graph of $~~r = a~\theta~~$ for $a=1$ and values of $\theta$ such that $0 \leq \theta \leq 4\pi$
We can see the graph in the window $[-15,15]$ by $[-15,15]$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/0ff18237-4973-4728-bf40-c526db307900/result_image/1555768857.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T000753Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=89a5c8f0cb346937284919a069c2e1c969255baa63351db6b1b04ecde96db648)
Work Step by Step
This is a graph of $~~r = a~\theta~~$ for $a=1$ and values of $\theta$ such that $0 \leq \theta \leq 4\pi$
Note that $r = 0$ when $\theta = 0$, and $r$ continues to increase as $\theta$ increases. This leads to a spiral shape.
At the endpoint of the spiral, $r = 4\pi$ when $\theta = 4\pi$
We can see the graph in the window $[-15,15]$ by $[-15,15]$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/0ff18237-4973-4728-bf40-c526db307900/steps_image/small_1555768857.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T000753Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=b2998e1226d7b0cf992378500ca77c222734f70468644e7efb027a9bf44d8868)