# How do you write the rectangular coordinates for the point: (4, 3π/2)?

Jan 21, 2016

Polar coordinates $\left(4 , \frac{3 \pi}{2}\right) \Leftrightarrow$ Rectangular coordinates $\left(0 , - 4\right)$

#### Explanation:

Any polar coordinate $\left(r , \theta\right)$ with $\theta = \frac{3 \pi}{2}$ and $r = 4$
$\textcolor{w h i t e}{\text{XXX}}$falls along the negative y-axis
$\textcolor{w h i t e}{\text{XXX}}$at a distance of $4$ from the origin.

Since this point is on the y-axis, $x = 0$
and
since it is a distance of $4$ down the y-axis from the origin, $y = - 4$