# How do you convert (1, 5pi/6) into rectangular coordinates?

Mar 21, 2016

$\left(- \frac{\sqrt{3}}{2} , \frac{1}{2}\right)$

#### Explanation:

Using the formulae that links Polar to Cartesian coordinates.

• x = rcostheta

• y = rsintheta

here r = 1 and $\theta = \frac{5 \pi}{6}$

hence : x$= 1 \times \cos \left(\frac{5 \pi}{6}\right) = \cos \left(\frac{5 \pi}{6}\right) = - \cos \left(\frac{\pi}{6}\right)$

and $y = 1 \times \sin \left(\frac{5 \pi}{6}\right) = \sin \left(\frac{5 \pi}{6}\right) = \sin \left(\frac{\pi}{6}\right)$

now the exact value of $\cos \left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$
and the exact value of $\sin \left(\frac{\pi}{6}\right) = \frac{1}{2}$

thus x =$- \cos \left(\frac{\pi}{6}\right) = - \frac{\sqrt{3}}{2}$
and y $= \sin \left(\frac{\pi}{6}\right) = \frac{1}{2}$