(1, −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) =

We know that

the relationship between the 2-dimensional polar and Cartesian coordinates is

r = √(x² + y²)
Θ = tan⁻¹ (y/x)
so
point  (1, -3)> this point belong to the IV quadrant
r = √(x² + y²) r = √(1² + (-3)²)> r=√10
Θ = tan⁻¹ (y/x) Θ = tan⁻¹ (3/1)> 71.57°
remember that the point belong to the IV quadrant
so
Θ=360-71.57> Θ=288.43°

the answer  is 
(r,Θ)=(√10,288.43°)