# What is the Cartesian form of (24,(15pi)/6))?

Dec 28, 2015

The Cartesian form of $\left(24 , \frac{15 \pi}{6}\right)$ is $\left(0 , 24\right) .$

#### Explanation:

Consider the figure. In this figure the angle is 22.6 but in our case

Let the Cartesian form of $\left(24 , \frac{15 \pi}{6}\right)$ be $\left(x , y\right) .$
Consider the figure. From figure:

$C o s \left(\frac{15 \pi}{6}\right) = \frac{x}{24}$

$\implies x = 24 C o s \left(\frac{15 \pi}{6}\right) = 24 \left(0\right) = 0$
$\implies x = 0$
Also from figure:

$S \in \left(\frac{15 \pi}{6}\right) = \frac{y}{24}$
$\implies y = 24 S \in \left(\frac{15 \pi}{6}\right) = 24 \left(1\right) = 24$
$\implies y = 24$

Therefore the Cartesian form of $\left(24 , \frac{15 \pi}{6}\right)$ is $\left(0 , 24\right) .$