Graphing Polar equations.notebook January 10, 2014

Transcription

1 graphing polar equations Ch.8 Lesson 2 1

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5 Target Agenda Purpose Evaluation TSWBAT: convert equations to polar, graph a polar equation on the polar plane by recognizing the forms Warm-Up/Homework Check Lesson Graph Matching BAT: Extend knowledge of graphing, apply knowledge to new situations, make connections to real world patterns

6 Converting between Polar equations and Rectangular What rectangular should look like: x 2 +y 2 = # or y = #x +# What polar should look like: r = #trigfunction... Tools for getting to a polar equation: 1)substitute rcosθ for x and rsinθ for y 2)solve for r (divide, subtract, factor) Tools for getting to a rectangular equation: 1)multiply by r to get r 2 or get a r in the first place or square both sides or complete the square 2) substitute x for rcosθ and y for rsinθ 3) When given an angle only, it looks like a line, use Tanθ, solve for y 6

7 Write each rectangular equaon in polar form

8 Write each polar equaon in rectangular form

9 Warm-Up: 3. Convert the equation to rectangular: r=4cscθ Find the rectangular coordinates for the point whose polar coordinate is ( 3,5π/6) Find the polar coordinates for the point whose rectangular coordinate is ( 6, 2) 9

10 Graphing a polar equation From a rectangular graph, we are graphing the distance from the x axis at each angle 10

11 Limacons r = a ± b cosθ r = a ± b sinθ Limacon with inner loop a < b Cardioid (heart shape) a = b Dimpled Limacon b< a< 2b Convex Limacon a > 2b 11

12 Rose Curves r = a cos nθ if n is odd # petals= n r = a sin nθ r = a cos nθ if n is even # petals= 2n r = a sin nθ 12

13 Circles r = a r = a cosθ r = a sin θ a Spiral r = aθ 13

14 Setting up your calculator! Mode: Float Degree Pol Connected Sequential Real Full Window: θmin=0 θmax=360 θstep=15 xmin= 4 xmax=4 ymin= 4 ymax=4 Go back to mode at the bottom: change to G T for graph and table 14

15 What type of graph is it? r=3 Circle cardioid on circle around positive with inner loop on pole dimpled rose on spiral convex rose off 15

16 What type of graph is it? r=sin3θ Circle circle around positive spiral cardioid on with inner loop on pole dimpled rose on convex rose off 16

17 What type of graph is it? r=2 + 2sinθ Circle circle around positive spiral cardioid on with inner loop on pole dimpled rose on convex rose off 17

18 What type of graph is it? r=1+2cosθ Circle circle around positive spiral cardioid on with inner loop on pole dimpled rose on convex rose off 18

19 What type of graph is it? r=3cosθ Circle cardioid on circle around positive with inner loop on pole spiral dimpled rose on convex rose off 19

20 What type of graph is it? r=cos4θ Circle cardioid on circle around positive with inner loop on pole spiral dimpled rose on convex rose off 20

21 What type of graph is it? r=1+3cos(3θ) Circle circle around positive spiral cardioid on with inner loop on pole dimpled rose on convex rose off 21

22 marizi TIME! 22

23 Graphing Polar equations.notebook Evaluation: the 1. Match equation to the graph 2. r=sin(θ/2) r=θsinθ r=1/ θ what should your x min, xmax, y min, and y max be? Practice! pg.548 #Do 1 skip 2 [1 8,15 32,35 40,60 66], 69 set calc window: θ min = 0, θ max = 720, step = 15 23