Converting polar equations to parametric

[riverjib]

Hello-- I have four equations I simply can't figure out:

r=cot(theta)csc(theta)
r=8sin(theta)
r=2cos(theta)sin(theta)
rsin(theta+pi/6)=2

I tried squaring each of these in hopes of finding something to work with, but I'm lost...please help!!

 

[galactus]

Use \(\displaystyle \L\\x=rcos({\theta}), \;\ y=rsin({\theta})\)

Sub your given r into them:

The first one:

\(\displaystyle \L\\x=\underbrace{cot({\theta})csc({\theta})}_{\text{r}}cos({\theta})=cot^{2}({\theta})\)

\(\displaystyle \L\\y=cot({\theta})csc({\theta})sin({\theta})=cot({\theta})\)

See?. Now, do the others.

 

[riverjib]

Figured it out!! Thank you anyway

My problem wasn't applying x=cros(theta) and y=rsin(theta)...I got that far (I did 35 other problems like these). I got stuck when there weren't enough r's...and just realized that I could multiply both sides by r.