10.2 Graphing Polar Equations Day 2 Today’s Date: 2/25/16

these points are on top of other points! EX 1: θ r 2.8 4 –2.8 –4 π θ r –2.8 –4 2.8 4 2π these points are on top of other points!

these points are on top of other points! EX 1: θ r 2.8 4 –2.8 –4 π θ r –2.8 –4 2.8 4 2π these points are on top of other points!

ROSES These look like flowers…we call each loop a “petal.” Length of each petal = ______ If b is even, there are _______ petals. If b is odd, there are _______ petals. (*Since the values from 0 to 2π give us the points, having b be an odd number, the values actually repeat themselves and overlap the already existing values so we do not get double the number of petals like we do with b being even.) First peak is at _______ Peaks are ______ radians apart (n is number of petals) Typical Graphs: a 2b b θ = 0

5 6 4 3 θ = 0 EX 2: Length of Petals:_______ Number of Petals:_______   EX 2: Length of Petals:_______ Number of Petals:_______   First Peak at:_______ Each Petal _______ rad apart EX 3: 5 6 4 3 θ = 0

EX 4: θ r ±2 ±1.4 und these points repeat

EX 4: θ r ±2 ±1.4 und these points repeat

Maximum distance out is ________ LEMNISCATE These look like “figure eights.” Oriented on _______________   Maximum distance out is ________ Typical Graph: polar axis

EX 5:   Oriented On: Polar Axis / Maximum Distance:_______    EX 6: 6 2

Ex 7: Determine an equation of the polar graph. Why?_________________________________________________ ______________________________________________________ r = 3cos 2θ petal graph w/ 4 petals  2θ peak on polar axis  cos petal length is 3  a = 3

Homework #1003 10-2 Day 2 Worksheet