91Ó°ÊÓ

Equations $r=3$and $r=-3$are identical in a polar coordinate system

Consider the equations $r=3$and $r=-3$.

The objective is to show that $r=3$and $r=-3$are identical in polar coordinate system.

The value 3 for the polar equation $r=3$describes the set of points $\left|3\right|$units from the pole.

Thus $r=3$is a circle with radius $\left|3\right|$centered at the pole.

Now for any real number $-3$the polar equation $r=-3$describes the set of points $\left|3\right|$units from the pole.

Thus $r=-3$is a circle with radius $\left|3\right|$centered at the pole.

Here 3 represents the length of the initial ray. that means the length of the initial ray is 3 units if $r=3$or $r=-3$since the length is positive.

That means the equations $r=3$and $r=-3$are same in polar coordinate system. Therefore $r=3$and $r=-3$are identical in polar coordinate system.

Hence the explanation.