Polar Coordinates And Rectangular Coordinates Worksheets (Page 4 of 7) in pdf

Polar Coordinates And Rectangular Coordinates Worksheets Page 4

5. Describe any changes that took place in these graphs.

6. Use the TRACE function to determine the largest and smallest distances from the pole. Does there appear any

way to determine those distances from the equation? How?

7. What happens when a is negative? Use any appropriate WINDOW.

8. What happens when b is negative? Use any appropriate WINDOW.

9. Now consider the graph of r = a + b cos

(you may have to adjust the range for some values of a and b). Do

the conjectures you made above hold true for cosine? If not, describe any differences you discovered.

10. We will now consider equations in which a = b. The equations of the form r = a + b sin

(a = b) form another type of curve called a cardioid (because it has a heart shape). Return to the Y= menu and

graph r = a + b sin

one at a time. With max = 360 and using x-values of

[-9.4,9.4] and an appropriate y-values, graph the following:

r = 4 + 4 sin

r = 5 + 5 sin

r = 2 + 2 sin

11. Make a generalization about the differences between the two types of limacons and the cardioid. Describe their

differences both graphically and as they relate to their equations.

12. Now consider the graph of r = a + bcos

. Do the conjectures you made above hold true for cosine? If not,

describe any differences you discovered.

13. Using your conclusions, sketch the graph of each of the following on polar graph paper without using your

graphing calculator. Check your answers with a graphing calculator.

a) r = 2 + 5cos

d) r = 3 - 3sin

b) r = 1 - 3sin

e) r = 6 + 3cos

c) r = -4 + 5cos

f) r = 4 - 2sin

1 2 3 4 5 6

Polar Coordinates And Rectangular Coordinates Worksheets Page 4