Given any Cartesian coordinates, (x,y), there are polar coordinates (r,θ) with −[π/2] \lt θ ≤ [π/2] .

Question

(a) If (x,y) = (2, 8) then (r, θ) = ( , ),

(b) If (x,y) = (18, 6) then (r, θ) = ( , ),

(c) If (x,y) = (−8, 7) then (r, θ) = ( , ),

(d) If (x,y) = (14, 0) then (r, θ) = ( , ),

(e) If (x,y) = (−7, −4) then (r, θ) = ( , ),

(f) If (x,y) = (0, −3) then (r, θ) = (

Answer 1

(x,y) -> (r,θ) .        r = sqrt(x^2 +y^2)  & θ = arctan(y/x) .