# Question #07bcc

Feb 17, 2017

Substitute $r \cos \left(\theta\right) \text{ for "x and rsin(theta)" for } y$, then write r as a function of $\theta$.

#### Explanation:

Substitute $r \cos \left(\theta\right) \text{ for "x and rsin(theta)" for } y$:

$5 r \cos \left(\theta\right) - 4 r \sin \left(\theta\right) = - 7$

Remove the common factor r:

$r \left(5 \cos \left(\theta\right) - 4 \sin \left(\theta\right)\right) = - 7$

Divide both sides by $5 \cos \left(\theta\right) - 4 \sin \left(\theta\right)$:

$r = \frac{- 7}{5 \cos \left(\theta\right) - 4 \sin \left(\theta\right)}$

Multiply numerator and denominator by -1:

$r = \frac{7}{4 \sin \left(\theta\right) - 5 \cos \left(\theta\right)}$