Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.3 Polar Coordinates - Exercises - Page 617: 8

$$\theta=\tan^{-1}\frac{1}{2}$$

We know that $y=x/2$. Convert to polar coordinates with $y=r\sin \theta$ and $x=r\cos \theta$. This gives $$r\sin \theta =\frac{r\cos\theta}{2}\Longrightarrow \tan \theta =\frac{1}{2}$$ Where we used the fact that $\tan \theta=\frac{\sin \theta}{\cos \theta}$. Thus we have: $$\theta=\tan^{-1}\frac{1}{2}$$