# What is the rectangular coordinate form of the polar coordinates (r, pi/6) ?

$\left(r , \frac{\pi}{6}\right)$ in polar form is $\left(\frac{\sqrt{3}}{2} r , \frac{r}{2}\right)$ in rectangular form
$\theta = \frac{\pi}{6}$ only gives you the angle.
You need a radius too, but $\left(r , \frac{\pi}{6}\right)$ in polar form is $\left(\frac{\sqrt{3}}{2} r , \frac{r}{2}\right)$ in rectangular form.
$\frac{\pi}{6}$ is one half of an internal angle of an equilateral triangle.