Question

The Cartesian coordinates of a point are given as.

(-6, 6) Find the polar coordinates (r,θ) of the point, where r > 0 and 0 ≤ θ < 2π.
(r,θ) = ____

Answer 1

The polar coordinates of the point (-6, 6) are θ < 2π.

(r,θ) =(6√2, -π/4).

Step-by-step explanation:

The polar coordinates (r, θ) of a point can be determined from its Cartesian coordinates (x, y) using the following formulas:

r = √(x^2 + y^2)

θ = arctan(y/x)

Using the Cartesian coordinates (-6, 6), we can calculate the polar coordinates as follows:

r = √((-6)^2 + 6^2) = √(36 + 36) = √72 = 6√2

θ = arctan(6/-6) = arctan(-1) = -π/4

Therefore, the polar coordinates (r, θ) of the point (-6, 6) are (6√2, -π/4).