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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