Q.30 - Calculus

Question

Graph the equations in Exercises 25–32 in the polar plane. Compare your graphs with the corresponding graphs in Exercises 17–24. 

$r=\theta , r\le 0$

Step-by-Step Solution

Answer

The required graph is as follows,

Step 1. Given Information.

The given polar equation is $r=\theta , r\le 0$.

Step 2. Explanation.

We have $r=\theta$. r  is negative so points are plotted in the diagonally opposite quadrant.

So, graph of the equation is as follows,

Step 3. Compare the graphs.

The graph of the equation in polar plane is spiral curve and the graph in $\theta r-$plane is as follows,