Question

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

Answer 1

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 [ - 8, -2 ]`.

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 ntheta and r =sin ntheta` 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

`( r, theta ) and ( r, theta + pi )` or

`( r, theta ) and ( r, theta - pi )`, for the opposite sense of

rotation/revolution.

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

`r = sqrt ( x^2 + y^2 )>= 0`.