# Math Help - quick polar coordinates question

1. ## quick polar coordinates question

In 3r = sin A, r and A represent polar coordinates, write each polar equation as an equation in rectangular coordinates (x,y).

thanks

2. $r=\sqrt{x^2+y^2}$ and $\displaystyle \tan A=\frac{y}{x}$.
We have $\displaystyle \sin A=\frac{\tan A}{\sqrt{1+\tan ^2A}}=\frac{y}{\sqrt{x^2+y^2}}$.
Replacing $r$ and $\sin A$ in the given relation, we have
$\displaystyle 3\sqrt{x^2+y^2}=\frac{y}{\sqrt{x^2+y^2}}\Leftright arrow 3(x^2+y^2)=y$

3. Hello, Andy!

I assume you know the conversion formulas:
. . $x \,= \,r\cos\theta,\;\;y \,= \,r\sin\theta,\;\;x^2 + y^2 \:=\:r^2$

In $3r \:= \:\sin\theta,\;\theta$ and $r$ represent polar coordinates.
Write the equation in rectangular coordinates $(x,y)$
$\text{We have: }3r \;=\;\sin\theta$

$\text{Multiply both sides by }r\!:\;\;3r^2 \;=\;\underbrace{r\sin\theta}$
. . . . . . . . . . . . . . $3\overbrace{(x^2+y^2)} \:=\:y$

4. thanks