10.2 Graphing Polar Equations Day 2

1. 10.2 Graphing Polar EquationsDay 2

2. Yesterday, we graphed polar equations using “brute force” – making tables of values. But this is very inefficient! We can bypass having to make all these separate calculations by learning some rules.  Symmetry – Tests for Symmetry on Polar Graphs If the following substitution is made and the equation is equivalent to the original equation, then the graph has the indicated symmetry.

3. EX 1: Identify the kind(s) of symmetry each polar graph possesses. A) PolePolar Axis B) PolePolar Axis

4. SPIRAL Also called the “Spiral of Archimedes” No special rules! Typical Graph:

5. CIRCLES There are three forms for a circle. pole pole pole polar axis k polar axis N E S W

6. EX 2: Radius:______ Center On: Polar Axis / Circle is N S E W of the pole 3

7. LIMAÇONSFrench for “snail.” OR (oriented on polar axis) (oriented on ) ±a a larger 2a a smaller larger diam inner loop smaller a a

8. Limaçon with Inner Loop Convex Limaçon Cardioid Oriented Oriented Oriented Diam: 6 Diam: 4 Larger: 6 Inner Loop: 2 Smaller: 2

9. ROSES These look like flowers…we call each loop a “petal.” a 2b b θ = 0

10. 5 4 4 3 θ = 0

11. LEMNISCATE These look like “figure eights.” polar axis

12. 2 2

13. Ex 10: Transform the rectangular equation into a polar equation and graph. Circle Radius 3 Center on N of pole

14. Ex 11: Determine an equation of the polar graph. r = 5 + 3sin θ r = 3cos 2θ Equation:____________________ Why?_______________________ ____________________________ ____________________________ Equation:____________________ Why?_______________________ ____________________________ ____________________________ on Dimpled Limiçon petal graph w/ 4 petals  2θ peak on polar axis  cos larger = 8 smaller = 2 bump hits at 5 a = 5, b = 3  a = 3 petal length is 3

15. Homework #1003 Pg 501 # 1–17 odd, 21, 23, 24, 27, 29, 31, 37, 41, 43, 44–47, 49–53 odd