Question

The cartesian coordinates of a point are given. (a) (−2, 2) (i) find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) = incorrect: your answer is incorrect. (ii) find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. (r, θ) = incorrect: your answer is incorrect. (b) (5, 5 3 ) (i) find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) = incorrect: your answer is incorrect. (ii) find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. (r, θ) = incorrect: your answer is incorrect.

Answer 1

The "r" coordinate is the square root of the sum of the squares of the rectangular coordinates.

The "θ" coordinate is the arctangent of the "y" coordinate divided by the "x" coordinate, taking quadrant into consideration.

(a) (-2, 2) ⇒ (√((-2)² +2²), arctan(2/-2)) = (2√2, 3π/4)

(b) (5, 5/3) ⇒ (√(5² +(5/3)²), arctan((5/3)/5)) = ((5/3)√10, arctan(1/3))
  ≈ (5.270463, 18.4349°)
  = (5.270463, 0.321751) . . . angle in radians