Question

The Cartesian coordinates of a point are given.

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

Answer 1

To find the polar coordinates (r, θ) of a point given its Cartesian coordinates (x, y), we use the formulas r = √(x² + y²) and θ = tan⁻¹(y/x). Applying these formulas to the point (6, -6), we find that its polar coordinates are (√72, -π/4).

Step-by-step explanation:

To find the polar coordinates (r, θ) of a point given its Cartesian coordinates (x, y), we use the following formulas:

• r = √(x² + y²)
• θ = tan⁻¹(y/x)

Using the given Cartesian coordinates (6, -6), we can substitute these values into the formulas:

r = √(6² + (-6)²)

= √(36 + 36)

= √72

θ = tan⁻¹((-6)/6)

= tan⁻¹(-1)

= -π/4

So, the polar coordinates of the point (6, -6) are (r, θ) = (√72, -π/4).