# What are the components of the vector between the origin and the polar coordinate (5, (-11pi)/6)?

Jan 27, 2018

We can use $x = r \cos \left(\theta\right)$ and $y = r \sin \left(\theta\right)$ to convert to the polar point to rectangular:

$x = 5 \cos \left(- \frac{11 \pi}{6}\right) = 5 \left(\frac{\sqrt{3}}{2}\right) = \frac{5 \sqrt{3}}{2}$
$y = 5 \sin \left(- \frac{11 \pi}{6}\right) = 5 \left(\frac{1}{2}\right) = \frac{5}{2}$

So the rectangular form is $\left(\frac{5 \sqrt{3}}{2} , \frac{5}{2}\right)$.

Since we're talking about the component form of the vector, the initial point is $\left(0 , 0\right)$.

The component form of the vector is $\left[\frac{5 \sqrt{3}}{2} , \frac{5}{2}\right]$.