Question

Change to polar coordinates the equation: $y=x\tan \alpha$

Answer 1

General form of polar co-ordinates $(r,\theta )$

where $r=\sqrt{x^2+y^2}$

$\theta ={\tan }^{-1}\left(\frac{y}{x}\right)$

Now in the given question

$y=x\tan \left(\alpha \right)$

$\Rightarrow \frac{y}{x}=\tan \left(\alpha \right)$

$\Rightarrow {\tan }^{-1}\left(\frac{y}{x}\right)=\theta =\alpha$

$\Rightarrow (r,\theta )=(r,\alpha )$