Question

The Cartesian coordinates of a point are given as (-2, 2). Find the polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π.

Answer 1

The polar coordinates of the point (-2, 2) are (2√2, -π/4).

Step-by-step explanation:

To find the polar coordinates (r, θ) of the point (-2, 2), we can use the following formulas:

r = √(x^2 + y^2)

θ = arctan(y/x)

Substituting the given values, we have:

r = √((-2)^2 + 2^2) = √(4 + 4) = √8 = 2√2

θ = arctan(2/(-2)) = arctan(-1) = -π/4

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