Question

Please help! what is the polar equation r = -5 theta in parametric form? thank you!

Answer 1

Use these equations when converting polar equations to parametric equations:

$x=r\cos\theta$

$y=r\sin\theta$

We know that $r=5\theta$, so substitute that into both equations for x and y.

$x=5\theta\cos\theta$

$y=5\theta\sin\theta$

Now, replace $\theta$ with any variable that you want to represent the parametric equations in. I'll use the standard variable, $t$

$x=5t\cos t$

$y=5t\sin t$

Thus, $r=5\theta$ represented in parametric form is:

$(x,y)=(5t\cos t, 5t \sin t)$

Let me know if you need any clarifications, thanks!

~ Padoru