Question

Write the equation in cartesian coordinates?

Answer 1

Write the equation of \[r = \theta \sin \theta\] in Cartesian coordinates.

Answer 2

I'm thinking multiply by r on both sides...
\[r^2 = \theta rsin \theta\]
Then that would give me \[x^2 + y^2 = \theta y\]
And there's still an extra theta :/

Answer 3

Yaaa I like that idea so far :O
Hmm that theta..

Answer 4

\[\large\rm \tan\theta=\frac{y}{x}\]err wait that's for the unitttttttt

Answer 5

no no no that's still true regardless of radial length, ya?
ya ya ya ya ya.

Answer 6

So ummm \(\large\rm \theta=\arctan\frac{y}{x}\), yes?

Answer 7

Yes, that's true.
Soooo... how would I use it though?

Answer 8

\[\large\rm x^2 + y^2 = y\color{orangered}{\theta}\]Like... this... I guess? :O\[\large\rm x^2 + y^2 = y\color{orangered}{\arctan\frac{y}{x}}\]I don't think there is anyway to solve this one for y. hmm

Answer 9

Hmmm interesting. Okay, I'll go with it. Thanks Zep!