Chapter 10b – Parametric Equations & Polar Graphing

1. Chapter 10b – Parametric Equations & Polar Graphing Paige McNaney, Luke Glaser, Freeman Judd

2. Vocabulary • Polar Curves: • Cardioids • Limacons • Rose Curves • Parametric Equations: • Parameter • Orientation • Polar Coordinate System: • Polar Coordinates • Polar Axis • π/2 Axis

3. Parametric Equations • Eliminate the parameter by isolating “t” or “cos/sin Θ” • Convert into Rectangular Equation • Graph: • Use increasing values of “t” • Use 0, π/2, π, 3π/2 & show orientation/ordered pairs • Projectile Motion

4. Polar Coordinates • Graph using (r, Θ) on the polar plane • Remember –r means graph in the opposite direction • Be able to find other representations • Convert into rectangular coordinates using: • x = r cos Θ • y = r sin Θ • Convert rectangular coordinates into polar using: • r2 = x2 + y2 • tan Θ = y/x • State r and Θ as positive values

5. Converting Equations • Polar -> Rectangular 1. If Θ = α, then take tangent of each side 2. If r = c, then square both sides 3. If r = a cos/sin Θ, multiply both sides by r • Rectangular -> Polar 1. Sub r cos Θ for x & r sin Θ for y 2. Sub r2 for x2 + y2 3. Solve for r

6. Polar Graphing • Lines: • 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…

7. Practice Problems • Pg 776 # 5, 11, 17, 22 • Pg 777 #57a • Pg 803 # 71, 75, 79, 87, 94, 96, 97