Name:_______________________ Date assigned:______________ Band:________

Precalculus | Packer Collegiate Institute

Shape of a Polar Graph

1. (a) Both cosr and sinr are circles. Discuss which one is symmetric around the x-axis and how you

know that.

(b) Explain why you only need to graph sinr from 0 to (and then the polar graph starts

repeating).

2. Draw a quick sketch of what 0.5r will look like. Pay attention to the negative sign.

3. For the following three equations, explain how many times the polar graph will hit the origin, and how you

know: 0 2

(a) 0 1cos .r (b) 2 3cos .r (c) s 1cor

4. (a) Without using algebra, but instead using conceptual arguments, can you find the center and radius of

4sinr … and explain how you did it?

(b) Without using algebra, but instead using conceptual arguments, can find the center and radius of

0.25cosr … and explain how you did it??

(c) Sketch both using desmos.com or the applet, and see if you were correct!

5. Draw a quick sketch of the following three equations in the blank box on the left. Your sketch is just that… a

sketch. it needs to get the general shape down. (Once you have made your prediction sketch, check your

answer with desmos.com or using the applet. Copy the correct answer on the graph on the box on the right.)

(a) sin 0.6r

(b) sin 1r

(c) 1 5sin .r

6. The graph for sin 0.2r is going to look slightly different from the graph of sin 0.6r (this is #5a).

Sketch what you think both of them are going to look like before graphing them. (Once you have made your

prediction sketch, check your answer with desmos.com or using the applet.)

0 6sin .r

0 2sin .r

7. (a) How are the graphs of cosr and cosr going to be different when graphed?

(b) Draw a sketch of both equations above, and for each, label the points where 0, , ,3

2 2

.

8. How many petals are the following polar graphs going to have?

(a) sin( )12r (b) cos( )13r (c) sin( )15r (d) sin( )16r