Question

Which set of polar coordinates describes the same location as the rectangular coordinates (-3,3)

Answer 1

The answer is (3sqrt2,135')

Apex

Answer 2

To convert from rectangular coordinates (x,y) to polar coordinates (r, θ), the following equations should be used:

r = sqrt( x^2 + y^2)
θ = tan^-1 (y/x)

Substituting (-3,3) accordingly to the equations, we obtain r equal to 3*sqrt(2) and θ equal to -π/4. Thus, the polar coordinates equivalent to (-3,3) is (3*sqrt(2), -π/4).