Question

The Cartesian coordinates of a point are given.

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

Answer 1

The polar coordinates for the Cartesian coordinates (-6, 6) are (6√2, (3/4)π), considering the point is located in the second quadrant.

Step-by-step explanation:

To find the polar coordinates (r, θ) of the Cartesian coordinates (-6, 6), we have to calculate the radius (r) and the angle (θ) in radians. The radius r is the distance of the point from the origin, which can be found using the formula r = √(x² + y²). In this case, r = √((-6)² + 6²) = √(36+36) = √72 = 6√2.

To find the angle θ, we take the arctan of the y-coordinate over the x-coordinate, arctan(y/x). However, since the point lies in the second quadrant, we must add π radians to the result of the arctan function to get the angle in the correct quadrant, which leads to θ = arctan(6/(-6)) + π = arctan(-1) + π = (-π/4) + π = (3/4)π. Therefore, the polar coordinates are (6√2, (3/4)π) where r > 0 and 0 ≤ θ < 2π.