Question

PLEASE HELP! POLAR COORDINATES

Answer 1

first of all
lets find one way to rewrite (5,-pi/6) with r>0
(5,-pi/6+2pi)
we can keep adding 2pi over and over


now let's rewrite (5,-pi/6) with r<0
well first let's think about the angle there
theta=-pi/6
that line looks like this:

also use a little imagination when it comes to my picture it is very sloppy
straingle lines have an angle measurement 180 deg

so -30 deg+180 deg=150 deg
or -pi/6+pi=5pi/6

so if we go on the on the opposite end of our line there
we will have to change the sign of r
so (5,5pi/6) is here



so again chaging the sign of r gives our point (-5,5pi/6)

so we wrote (5,-pi/6) two ways

(5,-pi/6+2pi) and (-5,-pi/6+pi)


see if this helps you answer your question