# What is the Cartesian form of (5,(3pi )/2)?

##### 2 Answers
Dec 23, 2017

The cartesian point is $\left(0 , - 5\right)$.

#### Explanation:

$x = r \cos \left(\theta\right)$ and $y = r \sin \left(\theta\right)$ and for the given point $r = 5$ and $\theta = \frac{3 \pi}{2}$.

$x = 5 \cos \left(\frac{3 \pi}{2}\right) = 5 \cdot 0 = 0$
$y = 5 \sin \left(\frac{3 \pi}{2}\right) = 5 \cdot \left(- 1\right) = - 5$

So the cartesian point is $\left(0 , - 5\right)$.

Dec 23, 2017

$\left(0 , - 5\right)$

#### Explanation:

$\text{to convert from "color(blue)"polar to cartesian form}$

$\text{that is "(r,theta)to(x,y)" where}$

•color(white)(x)x=rcostheta" and "y=rsintheta

$\text{here "r=5" and } \theta = \frac{3 \pi}{2}$

$\Rightarrow x = 5 \times \cos \left(\frac{3 \pi}{2}\right) = 5 \times 0 = 0$

$\Rightarrow y = 5 \times \sin \left(\frac{3 \pi}{2}\right) = 5 \times - 1 = - 5$

$\Rightarrow \left(5 , \frac{3 \pi}{2}\right) \to \left(0 , - 5\right)$