Polar Equations To Rectangular Equations, Precalculus, Examples And Practice Problems (2025-2026)

r=2cosθ→rcosθ=2r equals the fraction with numerator 2 and denominator cosine theta end-fraction right arrow r cosine theta equals 2 (Multiply by , substitute, isolate the radical, and square).

To switch from polar to rectangular, use these four relationships: 2. Examples (A horizontal line). Example 2: Converting Multiply both sides by r2r squared Substitute r2r squared over and complete the square: Result: A circle centered at with radius 3. Practice Problems Try converting these from polar to rectangular form: 4. Solutions (Quick Check) (Square both sides; (Apply tantangent to both sides; isolate the radical

tanθ=tanπ3→yx=3tangent theta equals tangent the fraction with numerator pi and denominator 3 end-fraction right arrow y over x end-fraction equals the square root of 3 end-root (Rewrite as (Apply tantangent to both sides