Short Answer

Sketch the curve with the given polar equation by first sketching the graph \({\rm{r}}\)as a function of \({\rm{\theta }}\)Cartesian coordinates.
\({\rm{r = 2 + sin\theta }}\)

The Curve is drawn with a polar equation by sketching a graph.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Draw a Graph\({\rm{y = 2 + sin\theta }}\).

Step 2: Draw a Graph\({\rm{r = 2 + sin\theta }}\).

First, make a Cartesian graph \({\rm{\theta }}\)at the horizontal axis and \({\rm{r}}\)the vertical axis. This is the transformation of \({\rm{y = sinx}}\)with amplitude 1, reflected over the \({\rm{X - }}\)axis and shifted up by 2 units. Therefore, \({\rm{r}}\)will vary between 1 and 3 and complete one cycle from zero to\({\rm{2\pi }}\).

To Plot the polar graph considers an increment of \({\rm{\pi /6}}\)approximately equal to\({\rm{0}}{\rm{.5236}}\).

\({\rm{\theta }}\)	\({\rm{r}}\)
0.0000	2.0000
0.5236	2.5000
1.0472	2.8660
1.5708	3.0000
2.0944	2.8660
2.6180	2.5000
3.1416	2.0000
3.6652	1.5000
4.1888	1.1340
4.7124	1.0000
5.2360	1.1340
5.7596	1.5000
6.2832	2.0000

Thus, the curve is drawn with the polar equation.

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Essential Calculus: Early Transcendentals

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Short Answer

Sketch the curve with the given polar equation by first sketching the graph \({\rm{r}}\)as a function of \({\rm{\theta }}\)Cartesian coordinates.
\({\rm{r = 2 + sin\theta }}\)

Step by Step Solution

Step 1: Draw a Graph\({\rm{y = 2 + sin\theta }}\).

Step 2: Draw a Graph\({\rm{r = 2 + sin\theta }}\).

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Essential Calculus: Early Transcendentals

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Short Answer

Sketch the curve with the given polar equation by first sketching the graph \({\rm{r}}\)as a function of \({\rm{\theta }}\)Cartesian coordinates.\({\rm{r = 2 + sin\theta }}\)

Step by Step Solution

Step 1: Draw a Graph\({\rm{y = 2 + sin\theta }}\).

Step 2: Draw a Graph\({\rm{r = 2 + sin\theta }}\).

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Sketch the curve with the given polar equation by first sketching the graph \({\rm{r}}\)as a function of \({\rm{\theta }}\)Cartesian coordinates.
\({\rm{r = 2 + sin\theta }}\)