[color=#000000]The applet below illustrates how to plot points whose coordinates are written in [b]POLAR FORM[/b]. [br]You can adjust the values of [/color][color=#0000ff][b]r[/b][/color][color=#000000] and [/color][color=#980000][b]theta[/b][/color][color=#000000] by using the sliders or the input boxes. [br](This grapher will only accept [/color][color=#980000][b]theta[/b][/color][color=#000000] values ranging from [/color][color=#980000][b]-2pi to 2pi[/b][/color][color=#000000]). [br][br]Slide the [b]black slider[/b] to illustrate how polar coordinates are plotted. [br][/color][br][color=#000000]Interact with this applet for a few minutes, then answer the questions that follow. [br][/color]

Use the interactive applet below that will allow you to plot polar functions of the form [math]\left(r,\theta\right)[/math]and answer the question 3 below the applet. [br][br]Try entering different functions into the input box in the top left hand corner. I would suggest looking at functions like[math]r=\sin(a\theta)[/math] ,[math]r=p-\cos(a\theta)[/math] ,[math]r=a\theta[/math] where [math]a,p\in\mathbb{R}[/math].[br][br]You may need to use the [math]\alpha[/math] symbol on the right [math]\theta[/math] of the input box to insert a [math]\theta[/math] in your function. When you have typed in your function press enter, you can then move the slider (in blue) to vary the size of [math]\theta[/math] .