# What is the Cartesian equivalent of polar coordinates (2, pi/6)?

Oct 2, 2014

$\left(r , \theta\right) \to \left(2 , \frac{\pi}{6}\right)$

$\left(x , y\right) \to \left(r \cos \left(\theta\right) , r \sin \left(\theta\right)\right)$

Substitute in $r$ and $\theta$

$\left(x , y\right) \to \left(2 \cos \left(\frac{\pi}{6}\right) , 2 \sin \left(\frac{\pi}{6}\right)\right)$

Remember back to the unit circle and special triangles.

$\frac{\pi}{6} = {30}^{\circ}$

$\cos \left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$

$\sin \left(\frac{\pi}{6}\right) = \frac{1}{2}$

Substitute in those values.

$\left(x , y\right) \to \left(2 \cdot \frac{\sqrt{3}}{2} , 2 \cdot \frac{1}{2}\right)$

$\left(x , y\right) \to \left(\sqrt{3} , 1\right)$