# How do you convert r= 45 / (5sin(t)+36cos(t))  into cartesian form?

Sep 1, 2016

$5 y + 36 x = 45$

#### Explanation:

The relation between Cartesian coordinates $\left(x , y\right)$ and polar coordinates $\left(r , t\right)$ is given by $x = r \cos \left(t\right)$ and $y = r \sin \left(t\right)$.

Hence, $r = \frac{45}{5 \sin \left(t\right) + 36 \cos \left(t\right)}$

$\Leftrightarrow 5 r \sin \left(t\right) + 36 r \cos \left(t\right) = 45$ or

$5 y + 36 x = 45$