# How do you graph the polar equation r=-5+3costheta?

Jul 21, 2018

Invalid equation that does not produce any non-negative r. I have been honoring Socratic graphic utility as precise, particularly in discarding pixels, when $r < 0$.

#### Explanation:

Here, $r = - 5 + 3 \cos \theta \in \left[- 8 , - 2\right]$.

It is high time that, globally, the practice of marking

points for negative r is no longer continued..

Importantly, the century old statement

If n is an even positive integer, the number of loops created by

$r = \cos n \theta \mathmr{and} r = \sin n \theta$ is 2n

has to be understood as inclusive of n r-negative loops.

It is all rotations and revolutions

For any antipodal ( diametrically opposite ) points

( x. y ) and ( - x, - y), the polar coordinates shall be

$\left(r , \theta\right) \mathmr{and} \left(r , \theta + \pi\right)$ or

$\left(r , \theta\right) \mathmr{and} \left(r , \theta - \pi\right)$, for the opposite sense of

rotation/revolution.

Forever, the length ( modulus ) of the position ( distance ) vector,

$r = \sqrt{{x}^{2} + {y}^{2}} \ge 0$.