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).
Polar to Rectangular Equations Converting equations between polar and rectangular isolate the radical
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; (Apply tantangent to both sides