for

Shanti Howard

Assignment 11

EMAT 6680
Polar Equations

Investigate --varying a, b, c, and k.

NOTE: This investigation will be an exciting and rewarding one, as I have never had any dealings with Polar Equations.

In this investigation, you and your partner (only one other person) will be expected to perform the following tasks:

Tell what polar equations are

How do they relate to parametric curves?

How do polar equations and their graphs relate to the "real world?"

How can we use polar equations to solve problems in the world?

Before you begin your exploration of some polar equations, here are a few guidelines to help you along the way:

1) a = n

2) k = k

3) t =

4) b = b

As you begin your journey through the hall of pictures, first, jot down any notes that you readily notice and any questions that you may have. Then, go back to each "picture," pause for a moment (that moment should be 5 to 15 minutes), and thoroughly examine each figure. What can you say about each? Where does the graph of each equation lie? How does its position in the Cartesian coordinate system have a relation to that of the other graphs? How are the equations of each graph similar? how are they different? How do you know this? Make a conjecture about your findings (your conjecture does not have to be the same as your partner's).

At the close of your journey, create your own graph that can go in the "hall of pictures." Be sure to include all of the above equations in your pictorial debut! CLICK HERE to go back to the list of equations.

Give proof to what you say...make sure your partner can "see" the same things you are seeing. Make sure that you and your partner can agree on the above questions. If there is any disagreeement, talk it out...if you two still cannot hash it out find out more information from other resources (e.g. other classmates). Then if all else fails, we will all discuss the matter in our class forum.

Figure 1

a = 0, k = 1, b = 1, c = 1

Figure 2

a = 1, k = 1, b = 1, c = 1

Figure 3

a = 6, k = 1, b = 1, c = 1

Figure 4

a = 10, k = 1, b = 1, c = 1

Figure 5

a = -1, k = 1, b = 1, c = 1

Figure 6

a = -6, k = 1, b = 1, c = 1

Figure 7

a = -10, k = 1, b = 1, c = 1

Figure 8

a = 0, k = 2, b = 2, c = 2

Figure 9

a = 0, k = 5, b = 5, c = 5

Figure 10

a = 5, k = 5, b = 5, c = 5

Figure 11

a = 0.4, k = 5, b = 5, c = 5

Figure 12

a = 0, k = 6, b = 7, c = 8

Figure 13

a = -2, k = -10, b = 7, c = 8

Figure 14

a = 0, k = -5, b = -1, c = -3

Figure 15

a = -1, k = -10, b = -10, c = -30

Figure 16

a = -1, k = -1, b = 1.14114111411114, c = 3.14

Figure 17

a = 0, k = -1, b = 1.14114111411114, c = 3.14

Figure 18

a = 3, k = 3.14, b = 3.14, c = 3.14

Figure 19

a = 3, k = 3.14, b = 3.14, c = 3.14, theta = 3.14

Figure 20

a = 5, k = 100, b = 100, c = 100

How was your journey through the hall of pictures? Hopefully, it was a pleasant and surprising one! Now CLICK HERE to go back to the top to fully begin your examination.

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