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5.1 Standard Angles 1 April 16, 2013 Photo by Hindrik S. http://www.flickr.com/photos/63991153@N00/6516894031 Unit5. Trigonometry
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5.1 Standard Angles
1
April 16, 2013
Photo by Hindrik S.
http://www.flickr.com/photos/63991153@N00/6516894031
Unit5.
Trigonometry
5.1 Standard Angles
2
April 16, 2013
NOT PART OF THIS COURSE
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3
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5.1 & 5.2 Definitions of Angles (Intro to Grade 12 Trig)
5.3 & 5.4 Sine & Cosine Laws
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Unit5.TrigonometryMentalMath
Setup thethreetrigonometricratiosfor θ.
θ
3
4
5
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5.1AnglesinStandardPosition
Anangleisformedbytworayswithacommonendpoint.
Anglesareoftenrepresentedas rotationsofaray.
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AnglesinStandardPosition
Anangleissaidtobeanangleinstandardpositionifitsvertexisattheoriginofacoordinategridanditsinitialarmcoincideswiththepositivex‐axis.
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E.g.Sketcheachangleinstandardposition.Statethequadrantinwhichtheterminalarmlies:
a.)36° b.)210° c.)315°
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ReferenceAngles
Foreachangleinstandardposition,thereisacorrespondingacuteanglecalledthereferenceangle.
Thereferenceangleistheacuteangleformedbetweentheterminalarmandthex‐axis.
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EgDeterminethereferenceangle θR foreachangle. Sketchinstandardpositionandlabelthereferenceangle.
a.)130° a.)300°
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Whataretheanglesinstandardpositionwithareferenceangleof20°?
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E.g.Determinetheangleinstandardpositionwhenanangleof40°isrelectedinthe:a.)inthey‐axisb.)inthex‐axisc.)inthey‐axisandtheninthex‐axis
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E.g.Determinetheangleinstandardpositionwhenanangleof40°isrelectedinthe:a.)inthey‐axisb.)inthex‐axisc.)inthey‐axisandtheninthex‐axis
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E.g.Determinetheangleinstandardpositionwhenanangleof40°isrelectedinthe:a.)inthey‐axisb.)inthex‐axisc.)inthey‐axisandtheninthex‐axis
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SpecialRightTriangles
Thereare3specialanglesinmathematics‐30°,45°,60°.
Theirtrigonometricratioshave exactvalues.E.g.Let'sindtheexactvalueofa45°‐45°‐90°trianglewithasidelengthof1unit.
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E.g.Findthetrigonometricratiosforthefollowingtriangle
1
2√3
30°
60°
sin60°=
cos60°=
tan60°=
sin30°=
cos30°=
tan30°=
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E.g.Allieislearningtoplaythepiano.Herteacherusesametronometohelpherkeeptime.Thependulumarmofthemetronomeis10cmlong.Foroneparticulartempo,thesettingresultsinthearmmovingbackandforthfromastartpositionof60°to120°.Whathorizontaldistancedoesthetipofthearmmoveinonebeat?Giveanexactanswer.
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Homeworkp8384#16`
