find the polar coordinates with rectangular coordinates?

Question

(-6,6) exact and 0
(1, -3) approx. and 0

Answer 1

Remember the identities:

x = rcosθ
y = rsinθ

r² = x² + y²

r² = (-6)² + 6² = 36 + 36 = 72
r = √72 = √(36*2) = 6√2

y = rsinθ
sinθ = y/r = 6 / (6√2) = 1/√2

θ = arcsin(1/√2) = 3π/4

(r, θ) = (6√2, 3π/4)
_____________________

r² = 1² + (-3)² = 1 + 9 = 10
r = √10

x = rcosθ
cosθ = x/r = 1/√10

θ = arccos(1/√10) ≈ 71.565051° ≈ 1.2490458 radians

(r, θ) = (1/√10, arccos(1/√10))