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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015121Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=a430d111ea4278db4c1f007888c50ee3f3e5efe2c85759ad3750b75ce3c97dd8)
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%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T015121Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=51f9c618fec714c79f943b60a520f090be9d7fa99174bc3215dd9e73d1dd7bc6)