Use these equations when converting polar equations to parametric equations:
[tex]x=r\cos\theta[/tex]
[tex]y=r\sin\theta[/tex]
We know that [tex]r=5\theta[/tex], so substitute that into both equations for x and y.
[tex]x=5\theta\cos\theta[/tex]
[tex]y=5\theta\sin\theta[/tex]
Now, replace [tex]\theta[/tex] with any variable that you want to represent the parametric equations in. I'll use the standard variable, [tex]t[/tex]
[tex]x=5t\cos t[/tex]
[tex]y=5t\sin t[/tex]
Thus, [tex]r=5\theta[/tex] represented in parametric form is:
[tex](x,y)=(5t\cos t, 5t \sin t)[/tex]
Let me know if you need any clarifications, thanks!
~ Padoru
