GRAPH A: 0.5r

Question 1: As you drag the green arrow, what gets graphed? Does it make sense? Explain in words why the resulting graph looks the way it does.

Question 2: How many “theta” does it take before the polar graph starts to repeat?

GRAPH B: 0.25r

Question 1: Before graphing, make a prediction as to what the polar graph will look like. Sketch it here…

Question 2: As you drag the green arrow, what gets graphed? Does it make sense? Explain in words why the resulting graph looks the way it does.

GRAPH C: 0.5r

Question 1: Look at how this equation looks different than graph B. Before doing anything, how do you think this polar graph will look when graphed? Sketch it

here…

Question 2: What is the distance between each loop of the spiral formed?

Question 3: For graph B, what is the distance between each loop of the spiral formed?

GRAPH D: ( )sinr

Question 1: You know from class that this is going to form a circle. Explain how you know whether it will be a circle “along the x-axis” or a circle “along the y-

axis”?

Question 2: It takes 2 radians for the parent sine graph to fully repeat. So explain as clearly as you can why the circle gets starts repeating at .

GRAPH E: ( )cosr

Question 1: You know from class that this is going to form a circle. Explain how you know whether it will be a circle “along the x-axis” or a circle “along the y-

axis”?

Question 2: If you wanted this circle to have a radius of 3, how would you modify the equation so that would happen? _______________________

GRAPH F: cos 0 5( ) .r

Question 1: Before doing anything, for 0 2 , guesstimate how many times the polar graph is going to hit the origin when it is being graphed.

Question2: Drag the green dot to where the function hits the x-axis. Look at what gets graphed in polar. Now drag the green dot a bit further to the next time

the function hits the x-axis. Look at what part that graphs in polar. Now drag the green dot to 2 . At that point the polar graph starts to repeat. Explain in

words what the part of the graph under the x-axis corresponds to in the polar graph.

GRAPH G: cos( ) 1r

Question 1: Before doing anything, for 0 2 , guesstimate how many times the polar graph is going to hit the origin… at what angles will this happen?

Question2: Drag the green dot to where the function hits the x-axis. Look at what gets graphed in polar. Now drag the green dot to 2 . At that point the polar

graph starts to repeat. Explain in words why the polar graph is not a circle. Then explain in words why the polar graph looks like it does.

GRAPH H: cos( ) 2r

Question 1: Before doing anything, for 0 2 , guesstimate how many times the polar graph is going to hit the origin… at what angles will this happen?

Question 2: Drag the green dot to the first valley. Is what is graphed a perfect semi circle? How do you know?

Question 3: Now drag the dot to the next peak. Now do you think what you have graphed is a perfect circle?

Question 4: Change the equation so it reads cos 1 1( ) .r or cos 1 3( ) .r . See what happens…

GRAPH I: co )s(r

Question 1: Make a prediction as to what this polar graph is going to look like. Sketch it here…

Question 2: Drag the green dot to the right to see the polar graph get formed. Is it what you thought? Explain in words why the polar graph looks like it does.

Question 3: Predict what si )n(r is going to look like. After you sketch your prediction, graph it. Were you right?

GRAPH J: sin )(2r

Question 1: How many times for 0 2 is the polar graph going to hit the origin?

Question 2: Drag the green dot to / 2 . What did that draw on the polar graph? Explain why it looks the way it does.

Question 3: DO NOT DRAG THE GREEN DOT. Make a prediction where the next part of the polar graph will appear if you dragged the green dot to … No

seriously, make a prediction. NOW drag the green dot to . Did your prediction math where the next part of the polar graph appeared?

Question 4: Finish dragging the green dot until the entire polar graph is complete. How many “theta” did it take before the graph was completed?

GRAPH K: cos )(3r

Question 1: Before graphing, make a prediction as to how many “theta” it will take before the polar graph is complete.

Question 2: Now that you’ve made your prediction, create the polar graph. How many “theta” did it take for the graph to repeat?

Question 3: What do you think would happen if you graphed sin )(3r --how do you think the polar graph would be different from the one you graphed

above? Once you make your prediction, graph it and see!

GRAPH K: sin )(4r

Question 1: How many times for 0 2 is the polar graph going to hit the origin?

Question 2: In graph J, you created a flower with a number of petals. How many petals do you think you are going to get for this flower?

Question 3: Graph a bunch of sin )(r k for different even and odd k values. Make a conjecture about the number of petals for when k is even. What about

for when k is odd? Now test your conjecture by changing the polar equation to see!