Question

The Cartesian coordinates of a point are given as (a) (-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 with Cartesian coordinates (-6, 6) are (6√2, 3π/4), with r representing the distance from the origin and θ the angle from the positive x-axis in radians.

Step-by-step explanation:

To find the polar coordinates of the point with Cartesian coordinates (-6, 6), we first calculate the distance of the point from the origin, which is the value of r, and then find the angle θ that the line from the origin to the point makes with the positive x-axis.

The distance r can be calculated using the Pythagorean theorem:

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

To find the angle θ, we note that the point lies in the second quadrant, where θ ranges from π/2 to π radians. Since the x and y coordinates are the same in magnitude, the angle is π/4 radians from the negative x-axis, making the angle π/4 + π/2 = 3π/4 radians.

Therefore, the polar coordinates of the point (-6, 6) are (r, θ) = (6√2, 3π/4).