Question

convert to rectangular form r= theta csc theta

Answer 1

please....Help me! :)

Answer 2

hmmm D:
not sure what to do about that silly theta in front.. thinking...

Answer 3

Using our identity for cosecant,\[\Large r=\theta \frac{1}{\sin \theta}\]
So we can multiply both sides by sin theta

Answer 4

\[\Large r \sin \theta=\theta\]

Answer 5

ok....and the\[\theta ??\]

Answer 6

hmmmm

Answer 7

I know that \[\theta=\tan^{-1} (\frac{ y }{ x } )\]

Answer 8

yah that's what i was thinking... looks so ugly though lol

Answer 9

do you understand how to simplify the left side?

Answer 10

I don't know :(

Answer 11

When going between Polar and Cartesian, try to remember these relationships:\[\Large x=r \cos \theta \qquad\qquad y=r \sin \theta\]

Answer 12

and?? how do you simplify??

Answer 13

\[\Large x=r \cos \theta \qquad\qquad \color{royalblue}{y=r \sin \theta}\]

So we have:\[\Large \color{royalblue}{r \sin \theta}=\theta\]
See the conversion on the left side? :)

Answer 14

Ya i think the right side just gives you\[\Large \arctan\left(\frac{y}{x}\right)\]as you initially thought

Answer 15

I'll call the smarty pants guys over to check though D:
@satellite73 @hartnn

Answer 16

ok...

Answer 17

this polar is a parabola

Answer 18

\[y ^{2}=x\]

Answer 19

really..? weird...
that's not what my graph is giving me :(
https://www.desmos.com/calculator/phsu8ovfbt

Answer 20

but I don't know how ....

Answer 21

very weird...

Answer 22

even i get r sin theta = theta as
y =x tan y
not parabola...