Fix the mistake: Polar Coordinates and Polar Equations

Polar Coordinates ① What Are Polar Coordinates?

The coordinates that represent a point using its distance r from the origin O (the pole) and its angle θ from the x-axis are called polar coordinates (r, θ).

Relationship with Cartesian coordinates:
　x = r cosθ, y = r sinθ
　r = √(x²+y²), tan θ = y/x

Example ① Express the polar coordinates (2, π/3) in Cartesian coordinates.
Solution: x = 2cos(π/3) = 1, y = 2sin(π/3) = √3
(1, √3)
Key Point
  • θ is usually defined by 0 ≦ θ < 2π or −π < θ ≦ π.
  • r is often taken to satisfy r ≧ 0.

Practice Problems

  1. Express the Cartesian coordinates (−1, √3) in polar coordinates.

Solutions and Explanations

  1. Solution: (2, 2π/3)

Math (Math C): related lessons