Question

A point has polar coordinates (r,Ф) and rectangular coordinates (x,y). If you know r and y, then:

Answer 1

well, let's say we know "r" and also "y", can we get the angle and the rectangular "x"?

$\bf \begin{cases} y=rsin(\theta )\\ x=rcos(\theta ) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ y=rsin(\theta )\implies \cfrac{y}{r}=sin(\theta )\implies sin^{-1}\left( \cfrac{y}{r} \right)=\theta$

and once we know what angle θ is, since x = rcos(θ), we know "r" already, and we know θ as well, so we know "x" as well.