change to polar form?

Question

a) (0, 8) 0 b) ( sq rt 3, 3)

Answer 1

Hi,

The point (0,8) is on the positive y axis. Therefore, it is clearly at the angle Pi/2 radians. Since it is 8 units away from the origin, polar form is (Pi/2, 8)

((sqrt(3),3)is such that if you take its y value divided by its x value and find the inverse tan of that, that it equals Pi/3 radians. Since you can do the Pythagorean Theorem
to find its distance from the origin, then c^2 = sqrt^2(3) + 3^2 = 3 + 9 = 12. If c^2 = 12, then c = 2sqrt(3). This is your distance from the origin.
In polar form you are at (Pi/3, 2sqrt(3))
I hope those help!! :-)

Answer 2

a) (x,y) = (0, 8)

r = √(x² + y²) = √(0² + 8²) = √64 = 8
y = rsinθ
sinθ = y/r = 8/8 = 1
θ = arcsin(1) = π/2

(r,θ) = (8, π/2) for 0 ≤ θ ≤ 2π
______________

b) (x,y) = (√3, 3)

r = √(x² + y²) = √[(√3)² + 3²] = √12 = 2√3
y = rsinθ
sinθ = y/r = 3/(2√3) = √3/2
θ = arcsin(√3/2) = π/3, 2π/3

(r,θ) = (2√3, π/3) and (2√3, 2π/3) for 0 ≤ θ ≤ 2π