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GeoGebra

Part 2

Author:Sidney Scott
Displayed is the unit circle.

Question 1

A. What is the center of the unit circle? B. What is the length of its radius? C. What are the x-intercepts? D. What are the y-intercepts? E. What is the formula given under the conic section (to the left of the graph) for the unit circle?

Manipulate the red slider ('r') and observe the results.

Question 2

A. What happens to the red circle as the value of 'r' increases and decreases? B. What kind of relationship do they have?

Adjust slider so that r=1.

Question 3

What value does the equation of circle 'c' equal?

Adjust slider so that r=2.

Question 4

What value does the equation of circle 'c' equal?

Adjust slider so that r=3.

Question 5

What value does the equation of circle 'c' equal?

Adjust slider so that r=4.

Question 6

What value does the equation of circle 'c' equal?

Adjust slider so that r=5.

Question 7

What value does the equation of circle 'c' equal?

Question 8

Use the data from Questions 3-7 to fill in the table below. When you have imputed all of your data, select cells A2-A6 and B2-B6. Then click on 'Polyline' (under the {1,2} tab).

Question 9

Notice how the graph plotted looks similar to a graph we have seen before. Which function does it resemble?

Question 10

What relationship do the values in the 'r' column have to the column?

Question 11

Based on the pattern you found in table, what is the general form for the formula of a circle with the center at A = (0,0)?

Once you have answered all the questions in Part 2, you may move on to Part 3.

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