Question

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

$r=1+\sin 3\theta$.

Short answer

The required graph is as follows,

Step-by-step solution

Step 1. Given Information.

The polar equation is$r=1+\sin 3\theta$.

Step 2. Explanation.

The equation is sine function with odd integer. It represent Rose with 3 petals. Here interval is $\left[0,\frac{\mathrm{\pi }}{2}\right]$.

Make a table to draw the curve.

$\theta$	0	$\frac{\pi }{18}$	$\frac{\mathrm{\pi }}{6}$	$\frac{\mathrm{\pi }}{3}$
$r=1+\sin 3\theta$	1	$\frac{3}{2}$	2	1

Step 3. Draw the graph.

The required graph is as follows,

Step 4. Compare the graph.

The graph of the equation in polar plane is a rose with three petals, and the graph of the equation in$\theta r-$plane is as follows,

As we have seen in both the graphs, it is observed that one graph is plotted in polar form and one graph is plotted in algebraic form. Both the graphs are different.