Question

Which of the following polar coordinates describes the same point as the point (5, -pi/6) given in polar coordinates?

a.) (5, pi/6)
b.) (-5, -pi/6)
c.) (5, 5pi/6)
d.) (-5, 5pi/6)
e.) none of these

Answer 1

you can get positive angles from negative by adding 2PI.
What is 2PI-pI/6? Answer 5pi/6

Answer 2

2pi - pi/6 = 11pi/6
that's not one of the choices.
But, 5pi/6 is, and 5pi/6 = 11pi/6 - pi, so switch the radius value of 5 to -5, which flips it through the origin.
So, D
If in doubt, just plot the points.