# How do you find the corresponding rectangular coordinates for the point ( 4, (3pi)/2 )?

##### 2 Answers
Jun 20, 2018

$\left(0 , - 4\right)$

#### Explanation:

$\left(4 , \frac{3 \pi}{2}\right) = \left(r , \theta\right)$

for Polars

$x = r \cos \theta$

$\therefore x = 4 \cos \left(\frac{3 \pi}{2}\right)$

$x = 4 \times 0 = 0$

$y = r \sin \theta$

$y = 4 \times \sin \left(\frac{3 \pi}{2}\right)$

$y = 4 \times - 1 = - 4$

$\left(0 , - 4\right)$

Jun 20, 2018

The coordinates are $\left(0 , - 4\right)$. See explanation.

#### Explanation:

To transform a point in polar coordinates $\left(r , \varphi\right)$ to Carthesian coordinates $\left(x , y\right)$ you use the formulas:

## $\left\{\begin{matrix}x = r \cos \varphi \\ y = r \sin \varphi\end{matrix}\right.$

In the given example we get:

$\left\{\begin{matrix}x = 4 \cos \left(\frac{3 \pi}{2}\right) \\ y = 4 \sin \left(\frac{3 \pi}{2}\right)\end{matrix}\right.$

$\left\{\begin{matrix}x = 4 \cdot 0 \\ y = 4 \cdot \left(- 1\right)\end{matrix}\right.$

So the answer is: