Use the mouse to adjust the sliders so that, a = 2, i = 2, b = 0, and c = 0 and then change the value of [b][i]t [/i][/b]from 0° to 360°. Which directions do A and C move as [i][b]t [/b][/i]changes from 0° to 360°? Now change value of [b][i]a [/i][/b]from 1 to 5. What do you see?

Set a = 2, b = 0, and c = 0. Then change the value of i from 1 to 2, to 3, … , to 10. Observe how the number of petals change as you change the value of i.[br]a. What is the corresponding value of[b][i] i[/i][/b] in the function r(x)? [br]b. What is the relationship between [b][i]i[/i][/b] and number of petals? [br]c. Can we create a shape with 6 or 10 petals?

Now set i = 1, b = 0, c = 1. [br]a. Then slowly change the value of a from 1 to 2. Describe the shape of the graph as the value of a change.[br][br]b. Then slowly change the value of a from 1 to 0. Describe the shape of the graph as the value of a change.

Now set a = 1, b = 0 and c = 1. As the value of [b][i]i[/i][/b] change from 1 to 5, observe how the number of petals change. [br]a. What is the relationship between [b][i]i[/i][/b] and number of petals? [br]b. Make your guess about the function that generates 6 or 10 petals. Check your conjecture by changing the value of[b][i] i[/i][/b]. Is the relationship between[b][i] i[/i][/b] and the number of petals the same as in Task 2.

Set a = c = 0 and b = 2. Do Task 2 and 3 replace [b][i]a[/i][/b] by [b][i]b[/i][/b] and [b][i]i[/i][/b] by [b][i]k[/i][/b].[br]What is the relationship between b and k in the function f(x) = b sin(kx) and the shape of the graph?