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Understanding Polar Coordinates
What are Polar Coordinates?
Polar coordinates represent points in a plane using a distance from a fixed point (the pole) and an angle from a fixed direction (the polar axis). This system is particularly useful for describing circular or spiral paths.
- r (radius) represents the distance from the origin
- θ (theta) represents the angle from the positive x-axis
- Coordinates are written as (r, θ)
- θ is typically measured counterclockwise from the positive x-axis
Conversion Formulas
Rectangular to Polar:
r = √(x² + y²)
θ = arctan(y/x)
Polar to Rectangular:
x = r × cos(θ)
y = r × sin(θ)
Applications
Physics
- Circular motion analysis
- Wave propagation
- Field theory
Engineering
- Radar systems
- Navigation
- Antenna design