Question

Which set of polar coordinates names the same point as (-5,pi/4)

Answer 1

In general, in polar coordinates (r, ω) = (-r, ω+π), because when you add π radians to an angle you are turning 180 degrees and then need to change the sign of the radius to preserve the original point.

Then (-5, π/4) = (5 , π/4 + π) = (5, 5π/4)

Answer: (5, 5π/4)