$\"\"$

(a)

The polar equation is $\"\"$ .

Since polar equation is a cosine function, it is symmetric with respect to the polar axis.

Construct a table and calculate the values of $\"\"$ on $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$
$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$	$\"\"$

Graph :

1. Draw a polar coordinate plane.

2. Use the points and polar axis symmetry to sketch the curve.

$\"\"$

(b)

The rectangular coordinates are $\"\"$ .

Find polar coordinates $\"\"$ .

Find $\"\"$ :

$\"\"$ .

Substitute $\"\"$ in the above equation.

$\"\"$

Find $\"\"$ :

$\"\"$

Since $\"\"$ , the angle is $\"\"$ .

Substitute $\"\"$ in the above equation.

$\"\"$

The sound originates from the point with polar coordinates $\"\"$ .

From the graph, this point does not lie within the polar region.

Hence the microphone will not detect the sound.

$\"\"$

(a)

Graph of the polar equation $\"\"$ is

$\"\"$

(b)

The sound originates from the point with polar coordinates $\"\"$ .

The microphone will not detect the sound.