# How do you convert r = 15 / (6sin(theta) + 43cos(theta))  into cartesian form?

Jun 24, 2016

$6 y + 43 x = 15$

#### Explanation:

Use (the transformation $\left(r \cos \theta , r \sin \theta\right) = \left(x , y\right)$.

The given equation becomes

$r = \frac{15}{6 \left(\frac{y}{r}\right) + 43 \left(\frac{x}{r}\right)}$

$= \frac{15 r}{6 y + 43 x}$

As $| 6 \sin \theta + 43 \cos \theta | \le \sqrt{{6}^{2} + {43}^{2}}$.,

$r \ge \frac{15}{\sqrt{{6}^{2} + {43}^{2}}}$. So, r does not become 0.

Cancelling the common factor r and cross multiplying,

$6 y + 43 x = 15$.