# How do you convert r = 16 / 3 -5 cos theta into cartesian form?

Jan 30, 2017

#### Explanation:

Here is the graph of $r = \frac{16}{3} - 5 \cos \left(\theta\right)$

Multiply both sides of the equation by r:

${r}^{2} = \frac{16}{3} r - 5 r \cos \left(\theta\right)$

Subsitute ${x}^{2} + {y}^{2} \text{ for } {r}^{2}$:

${x}^{2} + {y}^{2} = \frac{16}{3} r - 5 r \cos \left(\theta\right)$

Substitute $\sqrt{{x}^{2} + {y}^{2}}$ for r:

${x}^{2} + {y}^{2} = \frac{16}{3} \sqrt{{x}^{2} + {y}^{2}} - 5 r \cos \left(\theta\right)$

Substitute x for $r \cos \left(\theta\right)$

$\left({x}^{2} + {y}^{2}\right) = \frac{16}{3} \sqrt{{x}^{2} + {y}^{2}} - 5 x$

Here is a graph of the converted equation:

Please observe that the graphs are identical.