GetStarted!Do the following on your whiteboards. (1) Convert (-5, 8) to a polar coordinate. Use 0≤θ< 2π and r≥0. Round to the nearest tenth. (2) Name 3 other points that describe M(7, 240°) between -360°≤θ<360°.

CorrectU9H4Ask as many questions as you need!

Welcome!Homework: Finish investigations on U9L4 Updates: U9T (9.1-9.3, 9.5-9.6) will be Thursday (3/31)

Agenda1.  Get Started!

2.  Correct U9H4

3.  Announcements

4.  U9Q1

5.  Start U9L4

U9Q1Please reset your calculators:

2nd +, 7, 1, 2

You will be given 35 minutes to complete.

LearningObjectivesBytheendofthisperiodyouwillbeableto:① Graphpolarequations.

Real life polar equations!

http://www.intmath.com/blog/mathematics/polar-coordinates-and-cardioid-microphones-2496

9.2GraphsofPolarEquationsOneoftheapplicationsofpolargraphsistodescribethecharacteristicsofmicrophones.Differentmicrophoneshavedifferentrecordingpatternsdependingontheirpurpose.

9.2GraphsofPolarEquationsOmni-directionalMicrophone:Thismicrophoneisusedwhenwewanttorecordsoundfromalldirections(forexample,forachoir).Therecordingpatternisalmostcircularandwouldcorrespondtothepolarcurver=sinθthatwemetabove.

Bi-directionalMicrophone:Thisisusedinaninterviewsituation,wherewewanttopickupthevoicesoftheinterviewerandthepersonbeinginterviewed.

9.2GraphsofPolarEquations

ShotgunMicrophone:Thisisa"super-directional"mike,whereweonlywanttopickupsoundsfromdirectlyinfrontofthemike.Thegraphusedforthisexampleisr=θ2.

9.2GraphsofPolarEquations

TodaywearegraphingonourGraphingCalculatorsComplexPolarEquations.ChangingtoPolarEquations–Mode;switchtoPOLIwantyouinyourgroupstobegintheinvestigationbyfollowingthedirectionsandseriesofquestions.Thequestionsaretohelpyoucometoaconclusionaboutthetypesofequationsandideaofthepictures.

9.2GraphsofPolarEquations

#1Investigation

ameasurestheradius

Onthey-axis

Onthex-axis

#2Investigation

LeemuhSOHN

Onthey-axis

Onthex-axis

#2Investigation

Onthey-axis

Onthex-axis

AtypeofLimaconisaCardioid!

#3Investigation

#4Investigation

LehmNIHSkuht

Onthey-axis

Onthex-axisa2cos2θ

#5Investigation

9.2GraphsofPolarEquationsGobackthroughyournotesandhighlightallofthenamesofthepolarequations:Circle,Limacon,Cardiod,Lemniscate,rose,andSpiralofArchimedes.OnthenextslidewearegoingtotrytoidentifythesetypesofpolarequationsgivenagraphORequation.Ifyouaregivenagraphtellmewhethertheequationwouldcontainsineorcosine.

Whiteboards!

Whiteboards!

OverviewTake1minutetoindependentlythinkaboutthemostinterestingpartoftodayslesson.Shareyourinterestingthoughttoyourtablemates.Iwillcallonacoupleofyoutoshareyourinterestingthoughts.

TimingsGet Started: 8mins 10:56 1:14 Correct U9H4: 15mins 11:11 1:29 Announcements: 3mins 11:14 1:32 U9Q1: 40mins 11:54 2:12 U9L4: 35mins 12:29 2:47 Overview: 2mins 12:31 2:49

Table 1 Table 2 Table 3 Tyler Danny Leila Kayla Eliana JungWon Tonya John Yasmine

Table 4 Table 5 Table 6 Table 7 Collin Alden Josh W. Caley

Brenda Josh M. Nick Simmons Eden Andrew Wing Karen

Table 8 Table 9 Table 10 Table 11 Table 12

James B. Justin Avalon Matt Mike Aalia Ethan Kyra Mika Joey

Alyssa Aaron Megan

Table 1 Table 2 Table 3 MichaelV. Nat Cassie Jennifer Kelsey Nathalie Nirav Brandon Kelly

Table 4 Table 5 Table 6 Table 7

Joe Noah Kevin Emily Aaron Arthur Abdul Broneil Tam Aimee Baylee Sarah

Table 8 Table 9 Table 10 Table 11 Table 12 Allison Brad Anna Pranav Galen Lauren Ali Michael C. Jacob Bella

Sami Kasey Amelia