Mathematics

The key is recognizing that polar coordinates $r$ and $\theta$ relate to Cartesian coordinates through $x = r\cos\theta$ and $y = r\sin\theta$. Since $\tan\alpha$ is just a constant slope, substituting these relationships will let you express the line's angle in terms of $\theta$—the result should show that $\theta$ equals that constant angle, which is what a straight line through the origin looks like in polar form.

The key is recognizing that polar coordinates $r$ and $\theta$ relate to Cartesian coordinates through $x = r\cos\theta$ and $y = r\sin\theta$. Since $\tan\alpha$ is just a constant slope, substituting these relationships will let you express the line's angle in terms of $\theta$—the result should show that $\theta$ equals that constant angle, which is what a straight line through the origin looks like in polar form.