1 Apr 228:56 PM Section 13.2: General Angles and Radian Measure This section is divided up into 5 mini lessons that will all fit together in the end like a big puzzle. You might feel out of your comfort zone for a while, but stick with it...and study! Apr 2210:15 PM A. Angles in Standard Position • In the last section, we just worked with acute angles in triangles. • Now, we will branch out to angles with a measure of any real number. • This requires some new vocabulary terms.
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Apr228:56PM
Section13.2:GeneralAnglesandRadianMeasure
Thissectionisdividedupinto5minilessonsthatwillallfittogetherintheendlikeabigpuzzle.
Youmightfeeloutofyourcomfortzoneforawhile,butstickwithit...andstudy!
Apr2210:15PM
A.AnglesinStandardPosition
Inthelastsection,wejustworkedwithacuteanglesintriangles.
Now,wewillbranchouttoangleswithameasureofanyrealnumber.
Thisrequiressomenewvocabularyterms.
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Apr228:58PM
Wewillstart"mapping"anglesonacoordinateplane.
Apr229:02PM
Ex.1:Let'sdrawsomeanglesinstandardposition.
a.210
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Apr229:08PM
b.45 c.510
Apr229:09PM
B.CoterminalAngles
Twoanglesarecoterminaliftheirterminalsidescoincide.
Inthepreviousexample,150and510arecoterminal.
Whatisthenumericrelationshipbetweenthesetwomeasures?
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Apr229:15PM
Ex.2:Findonepositiveandonenegativeanglethatiscoterminalwiththegivenangle.
a.60
b.495
Apr229:17PM
LearningOpportunityforthissectionsofar:(yes,therewillbemore.)
p.8625#1,3,4,69,14,1518,5561odd
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Apr229:26PM
C.RadianMeasure
Sofar,theonlywayyouhavemeasuredanglesisbydegrees.Youcanmeasureanangleusingaprotractortodetermineitsmeasure.
AnotherwaytomeasureanangleistouseRadianMeasure.Itisawaytomeasureananglebythelengthofitsarc.Intheory,youcouldmeasuretheanglewithatapemeasure(cmorin).
Apr229:32PM
DefinitionofaRadian:
Oneradianisthemeasureofanangleisstandardpositionwhoseterminalsideinterceptsanarcof
lengthr.
Sowhatdoesthismean?
SMART Notebook
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Apr229:37PM
So,somealgebratounderstandtheconceptofradians:
360 = CircumferenceofaCircle
360 = 2r
Inaunitcircle,wesettheradius=1Therefore
360 = 2radians(Thisisalength)
Apr229:45PM
a.Sowhatis180inradians?
b.90?
c.45?
Hereisthegeneralwaywecanconvertfromradianstodegreesandviceversa.
RD =
180
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Apr229:50PM
Ex.3:Convertingbetweenradiansanddegrees.
Apr229:52PM
D.Let'sputthewholelessontogether!
Youneedtobeableto:
Drawanangle(indegreesorradians)instandardposition.
Findpositiveandnegativecoterminalanglesgivenanangleineitherdegreeorradianmeasure
Convertbetweendegreeandradianmeasure
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Apr229:57PM
Ex.4.
a.
Tip:Workwithmeherewiththefractions.Youhavetothinkinradians.
Apr2210:00PM
b. c.
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Apr2210:03PM
LearningOpportunity#2:(yes,thereisonemoreminilesson)
p.8625#5,1013,1922,2331
Apr2210:09PM
E.ArcLengthandAreaofaSector
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Apr2210:10PM
Ex.5
Apr2210:10PM
FinalLearningOpportunity:
p.863#3238
p.865Quiz1(Toprepareforyour13.113.2Quiznextclass.)
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Apr98:48AM
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Attachments
ExplainingPI.gsp
SMART Notebook
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