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Grade 12 Math Lab: Analysis & Inference FREE
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Polar Coordinates & Curves
Learning Objectives
- Convert between polar and Cartesian
- Graph polar curves
- Find areas in polar
Key Concepts
Polar Coordinates
(r, θ) where r is distance from origin, θ is angle
Rose Curve
r = a·cos(nθ) or r = a·sin(nθ)
Theory
**Conversions:**
- x = r·cosθ, y = r·sinθ
- r = √(x² + y²), θ = arctan(y/x)
**Common polar curves:**
- Circle: r = a
- Rose: r = a·cos(nθ) — n petals if n odd, 2n if n even
- Cardioid: r = a(1 + cosθ)
- Limaçon: r = a + b·cosθ
**Area:** A = ½∫[α,β] r² dθ
Examples
Convert (3, π/4) to Cartesian
Solution: x = 3cos(π/4) = 3√2/2, y = 3sin(π/4) = 3√2/2