(1 point) (a) The Cartesian coordinates of a point are (1,1). (i) Find polar coordinates (r,θ) of the point, where r>0 and 0≤θ<2π. r= θ= (ii) Find polar coordinates (r,θ) of the point, where r<0 and 0≤θ<2π. r= θ= (b) The Cartesian coordinates of a point are (23–√,−2). (i) Find polar coordinates (r,θ) of the point, where r>0 and 0≤θ<2π. r= θ= (ii) Find polar coordinates (r,θ) of the point, where r<0 and 0≤θ<2π.

Answer:P(1, π/4)P(-1, π/4)P(4, 5π/6)P(-4, 5π/6)Step-by-step explanation:Knowing the formulasr = √(x²+y²)θ = Arctg (y/x)we havea) P(1, 1) i)  r = √(1²+1²) = +1r = +1θ = Arctg (1/1) = π/4P(1, π/4)ii) r = √(1²+1²) = -1r = -1θ = Arctg (1/1) = π/4P(-1, π/4)b) P(2√3, -2) i)  r = √((2√3)²+(-2)²) = +4r = +4θ = Arctg (-2/2√3) = 5π/6P(4, 5π/6)ii)r = √((2√3)²+(-2)²) = -4r = -4θ = Arctg (-2/2√3) = 5π/6P(-4, 5π/6)