Chapter 10b – Parametric Equations & Polar Graphing

Paige McNaney, Luke Glaser, Freeman Judd

VocabularyPolar Curves:1. Cardioids2. Limacons3. Rose Curves

Parametric Equations:1. Parameter2. Orientation

Polar Coordinate System:1. Polar Coordinates2. Polar Axis3. π/2 Axis

Parametric EquationsEliminate the parameter by isolating “t” or

“cos/sin Θ”Convert into Rectangular EquationGraph:- Use increasing values of “t”- Use 0, π/2, π, 3π/2 & show

orientation/ordered pairsProjectile Motion

Polar CoordinatesGraph using (r, Θ) on the polar plane- Remember –r means graph in the opposite

direction- Be able to find other representationsConvert into rectangular coordinates using:1. x = r cos Θ2. y = r sin Θ Convert rectangular coordinates into polar using:1. r2 = x2 + y2

2. tan Θ = y/x3. State r and Θ as positive values

Converting EquationsPolar -> Rectangular1. If Θ = α, then take tangent of each side2. If r = c, then square both sides3. If r = a cos/sin Θ, multiply both sides by rRectangular -> Polar1. Sub r cos Θ for x & r sin Θ for y2. Sub r2 for x2 + y2

3. Solve for r

Polar GraphingLines:- Θ = α forms…- r = a/sin Θ forms…- r = b/cos Θ forms…Circles:- r = a center & radius are…- r = a cos Θ center & radius are…- r = a sin Θ center & radius are…

Practice ProblemsPg 776 # 5, 11, 17, 22Pg 777 #57aPg 803 # 71, 75, 79, 87, 94, 96, 97