14. Polar Coordinates

Question 1

Polar coordinates

(r,θ)

Answer 1

Represents a point in terms of its distance from the origin and the angle between the positive x-axis and the ray connecting the point to the origin.

Question 2

Relationship between rectangular and polar coordinates

(x,y) and (r,θ)

Answer 2

x = r cosθ

y = r sinθ

x² + y² = r²

Question 3

A point in the plane represented by (r,θ) can also be represented by…

Answer 3

(r, θ + 2n π)

or

(–r, θ + (2n – 1) π)

where n is an integer