I need to show this equation
$r = \cot(\theta)$ as $x$,$y$ using the following laws:
$x=r\cos(\theta)$, $y=r\sin(\theta)$
$r^2=x^2+y^2$, $\tan(\theta)=\frac{y}{x}$
This is what I've done :
$$r = \cot(\theta) \\
r = \frac{\cos(\theta)}{\sin(\theta)} \\
r^2=\frac{r\cos(\theta)}{\sin(\theta)}\\
x^2+y^2=\frac{x}{\sin(\theta)}$$
Now, I'm stuck what should I do with $\sin(\theta)$?
Any ideas?
Thanks!
Best Answer
You can also use
$$r=\sqrt{x^2+y^2}$$
and $$\cot{\theta}=\frac{x}{y}$$
instead.