Chapter 9.6, Problem 65E

(a)

To determine

To graph:

The graph of the model and identify the type of graph.

Explanation of Solution

Given information:

Polar equation $r=5+5\cos \theta$

Graph:

  

Interpretation:

The graph is model is drawn as above.

The sound pickup pattern modeled by

  $r=5+5\cos \theta$

Here, $\left|r\right|$ represents how sensitive microphone is to sounds.

Type of curve us Limacons.

Here $\frac{a}{b}=\frac{5}{5}=1$ , so curve is heart shaped.

(b)

To determine

The angle of microphone that has sensitive sound.

Answer to Problem 65E

The angle of microphone that has sensitive sound is $\theta =0$ radians.

Explanation of Solution

Given information:

Polar equation $r=5+5\cos \theta$

Calculation:

The polar equation is $r=5+5\cos \theta$

Here $\left|r\right|$ is a maximum for $\theta =0$ .

For $\theta =0$ , the value of $r$ is

  $r=5+5\cos \left(0\right)\to r=10$

Thus, the microphone is most sensitive for $\theta =0$ radians.