Chapter 9: Q. 32 (page 747)

Graph the equations in Exercises 25–32 in the polar plane. Compare your graphs with the corresponding graphs in Exercises 17–24.
$r = 1 + \sin 3 θ$ .

Short Answer

Expert verified

The required graph is as follows,

Step by step solution

Step 1. Given Information.

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

Step 2. Explanation.

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

Make a table to draw the curve.

$θ$	0	$\frac{π}{18}$	$\frac{π}{6}$	$\frac{π}{3}$
$r = 1 + \sin 3 θ$	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 $θ r -$ 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.

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Graph the equations in Exercises 25–32 in the polar plane. Compare your graphs with the corresponding graphs in Exercises 17–24.
$r = 1 + \sin 3 θ$ .

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Draw the graph.

Step 4. Compare the graph.

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Graph the equations in Exercises 25–32 in the polar plane. Compare your graphs with the corresponding graphs in Exercises 17–24.r=1+sin3θ.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Explanation.

Step 3. Draw the graph.

Step 4. Compare the graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Calculus

Decision Maths

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Graph the equations in Exercises 25–32 in the polar plane. Compare your graphs with the corresponding graphs in Exercises 17–24.
$r = 1 + \sin 3 θ$ .