BC 3Name:

Polar 2: A Re-View of Polar Graphs

Now that we’ve reacquainted ourselves with polar coordinates, let's have another look at some of the different types of polar graphs. Before we begin, you will need to change the Graph mode of your calculator from FUNCTION to POLAR. In addition, in the Y= editor, select r1=, press 2nd F1 (F6 Style), and select 6:Path. This will allow you to follow polar graphs as they are traced out.

r = a cos( or r = a sin(

Use your calculator to draw a number of graphs of this form (for example, r = 2cos  or r = 5sin ) until the pattern is clear to you. Then sketch one or two of each type of graph, along with their respective equations, in the space below, noting the intercepts clearly.

1.What kind of geometric figure do you get?

2.Forr = a cos(, what are the coordinates of the center and radius? What about for r = a sin()?

3.As  goes from 0 to 2, how many times is the figure traced out?

Polar 2.1F12

Limaçons: r = a±b sin( or r = a±b cos( with a > 0 and b > 0

Use your calculator to draw a number of graphs of this form (for example, r = 2 + 3 sin( or

r = 5 – 2 cos() until the patterns are clear to you. Then sketch one or two of each type of graph, along with their respective equations, in the space below, noting the intercepts clearly.

1.Consider graphs of the form r = a ± b cos(). Describe these graphs, including intercepts and special features of the graphs, when:

a.a = b. (You may recall that these special limaçons are called cardioids.)

b.ab.

c.ab.

2.What happens to each of the above graphs when the form is changed to r = a ± b sin( ?

3.With either form, as  goes from 0 to 2, how many times is the figure traced out?

Rose Leaves: r = a cos(n) or r = a sin(n), where nZ+.

Use your calculator to draw a number of graphs of this form (for example, r = 5 sin(2 or r = 2 cos(3) until the patterns are clear to you. Then sketch one or two of each type of graph, along with their respective equations, in the space below, noting the intercepts clearly.

1.Consider graphs of the form r = a cos(n):

a.If n is odd,

i.how many “petals” are there?

ii.how many times is the figure traced out as  goes from 0 to 2?

b.If n is even,

i.how many “petals” are there?

ii.how many times is the figure traced out as  goes from 0 to 2?

c.What does the constant "a" determine?

2.What happens to the graphs when the form is changed to r = a sin(n?

3.Describe how one might look at a rose leaf graph and quickly determine which function (sine or cosine) was used.

Polar 2.1F12