Find three additional polar representation of the point (-3, pie over 6) given in polar coordinates,using -2 pie <0 <2pie.

All you have to do is find coterminal angles or else

change the -3 to +3 and state the angle which goes in the opposing direction

eg. (-3,π/6) or (3, 7π/6)

to get coterminal angles just add 2π to your angle

e.g (-3,π/6) and (-3, 13π/6) puts you in the same spot

To find three additional polar representations of the point (-3, π/6), we can use the fact that angles can be rotated by multiples of 2π and the distance or magnitude remains the same.

Given that -2π < 0 < 2π, let's find three additional angles that fall within this range and calculate their corresponding polar representations.

1. Angle: (π/6 + 2π) = 13π/6
The magnitude (-3) remains the same.
Polar Representation: (-3, 13π/6)

2. Angle: (π/6 + 4π) = 25π/6
The magnitude (-3) remains the same.
Polar Representation: (-3, 25π/6)

3. Angle: (π/6 + 6π) = 37π/6
The magnitude (-3) remains the same.
Polar Representation: (-3, 37π/6)

Therefore, the three additional polar representations of the point (-3, π/6), within the given range, are:
(-3, 13π/6), (-3, 25π/6), and (-3, 37π/6).