Answer
$\theta = 45^\circ$
There are infinite possibilities (i.e. $−135^\circ, 225^\circ$, ......), for $\theta = 45^\circ$ is just one of them.
Work Step by Step
$y = x$
$rsin\theta = rcos\theta$
$\frac{rsin\theta}{rcos\theta} = 1$
$tan\theta = 1$
$\theta = 45^\circ$
There are infinite possibilities (i.e. $−135^\circ, 225^\circ$, ......), for this $\theta = 45^\circ$ is just one of them.
Thus, one way to translate the equation y = x to polar coordinates is to convert it to $\theta = 45^\circ$.
