a.

A ceiling fan has a central motor with blades that each extend  units from the center.

The shape of the fan can be represented by a rose curve.

A rose curve has a form of  or .

Where is an integer.

For a rose with petals (Here Petals represents blades) ,.

For a rose with petals that are units long ,.

Therefore polar equations that can be used to represent this fan are and .

b.

Because is a function of the cosine function, it is symmetric with respect to the polar axis.

For the graph of  on .

when .

when .

Interpreting these results in terms of the polar equation ,

we can say that has a maximum value of when and

when .

Since the function is symmetric with respect to the polar axis, make a table and calculate a few additional values

of  on .

 Use these points and symmetry to sketch the graph of the function :

(1).Draw the table.

(2).Draw the polar cordinate.

(3).Graph the function.

Graph :

Because is a function of the sine function, it is symmetric with respect to the line .

For the graph of  on .

when .

when .

Interpreting these results in terms of the polar equation ,

we can say that has a maximum value of when and

when .

Since the function is symmetric with respect to the line , make a table and calculate a few additional values

of  on .

Use these points and symmetry to sketch the graph of the function :

(1).Draw the polar cordinate.

(2).Graph the function.

 Graph :

a.

Polar equations that can be used to represent this fan are and .

b.

Graph of :

Graph of :