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

Mar 21, 2018

$\left(x , y\right) \equiv \left(- 5 , 0\right)$

#### Explanation:

Given:
$r = 5$
$\theta = \pi$

$x = r \cos \theta$
$\implies r \cos \theta = 5 \cos \pi$
$\implies \cos \pi = - 1$
$\implies 5 \cos \pi = 5 \times - 1$
$\implies r \cos \theta = \textcolor{b l u e}{- 5}$

$y = r \sin \theta$
$\implies r \sin \theta = 5 \sin \pi$
$\implies \sin \pi = 0$
$\implies 5 \sin \pi = 5 \times 0$
$\implies r \sin \theta = \textcolor{b l u e}{0}$

$\left(x , y\right) \equiv \left(- 5 , 0\right)$