a.

The equations are

The equations and are in the form of , where in both the equations and .

Notice that since equation is a reflection of equation

in the line .

Therefore, each equation represents a special limaçon called a Cardioid.

b.

Because each polar equation is a function of the cosine function, each is symmetric with

respect to the polar axis.

Therefore, make a table and calculate the values of on .

Table :

(1) Draw the polar grid.

(2) Graph the functions and on the same graph.

Graph :

c.

Observe the Graph :

The overlapping areas of the two graphs indicate regions where sound will be detected by both microphones.

For example, sounds made up to  units directly north or south of the microphones will be detected by both microphones.

Also, each microphone will detect sound up to units away directly in front it.

a.

Each equation represents a special limaçon called a Cardioid.

b.

Graph :

c.

Each microphone will detect sound up to units away directly in front it.