Question

(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 1

P(1, π/4)

P(-1, π/4)

P(4, 5π/6)

P(-4, 5π/6)

Explanation:

Knowing the formulas

r = √(x²+y²)

θ = Arctg (y/x)

we have

a) P(1, 1)

i)

r = √(1²+1²) = +1

r = +1

θ = Arctg (1/1) = π/4

P(1, π/4)

ii) r = √(1²+1²) = -1

r = -1

θ = Arctg (1/1) = π/4

P(-1, π/4)

b) P(2√3, -2)

i)

r = √((2√3)²+(-2)²) = +4

r = +4

θ = Arctg (-2/2√3) = 5π/6

P(4, 5π/6)

ii)

r = √((2√3)²+(-2)²) = -4

r = -4

θ = Arctg (-2/2√3) = 5π/6

P(-4, 5π/6)