polar coordinates 1

Question

Determine two pairs of polar coordinates for the point (5, -5) with 0° ≤ θ < 360°.

Answer 1

Calculate the magnitude:

r = √((5)^2+(-5)^2)

   =√50

    = 5√2

Calculate the angle:

θ = tan^-1 (-5/5)      a>0

    = tan^-1 (-1)

  = tan^-1 (-5/5)

 = 3pi/4,7pi/4

Polar coordinates

r(cosθ+isinθ)=5√2(cos 3pi/4+isin 3pi/4)

                    =5√2(cos 7pi/4+isin 7pi/4)