Question

Given the rectangular coordinates (2,-2√3), which of the following polar coordinate pairs in radians represents the same point?

a. (-4, 2π/3)
b. (4, 4π/3)
c. (-2, π/3)
d. (2, 5π/3)

Answer 1

The magnitude of this point is
`\sqrt{2^2+(-2√(3))^2} = √(16) = 4`, so the magnitude is four.

We can finish the solution by trying the only two answers with magnitude four: A and B.

For option B, the rectangular coordinates are
`(4 \cos (4\pi)/(3), 4 \sin (4\pi)/(3)) = (-2, -2√(3))`, so B is incorrect.

For option A, the rectangular coordinates are
`(-4 \cos (2\pi)/(3), -4 \sin (2\pi)/(3)) = (2, -2√(3))`, so the answer is A.