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HONORS PRECALCULUS:UNIT 7 NAME ___________________________________ DAY 1NOTES: BEGINNING TRIGONOMETRY DATE ________________________ PERIOD ______ TRIGON: METRON: I. REVIEWING SINE AND COSINE GRAPHS Use your knowledge of basic transformations to graph the following (LABEL THE AXES appropriately): 1) 2) 3) 4) 5) 6) 2 sin - = x y x y sin 3 - = 3 cos + = x y x y cos 4 = x y cos - = 1 sin 2 + = x y Triangle measure Iai a midline o Gi d too at a vertical a FETE Eiqo are ay stretchgofink Ifull Period I vertical y asin bx C td shift UBoorwn r midline Vertical Shift is 2 Down 2 I l I l l l a E E t ea 0 midline up 3 EFFETE O P I I l I l za in In Y I Tak Iz Iz'm 2 2 Midline verticalstretch Up 1 of 2 iIH I za 54in za Y tf i IaI Iii Z 2

measure Iai - Weebly...%8q!!'=02!>1! yz[ \]^y \!u!!!!"""# $ %&"%'!, t%! ()! *+%!,-"*!. "$./%!"-)($_`*"(-g! o1!p>7!>70815!q410=a370 r!;asa7;!%f#t(!b737 u:1pav>9h!s>9410r!

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Page 1: measure Iai - Weebly...%8q!!'=02!>1! yz[ \]^y \!u!!!!"""# $ %&"%'!, t%! ()! *+%!,-"*!. "$./%!"-)($_`*"(-g! o1!p>7!>70815!q410=a370 r!;asa7;!%f#t(!b737 u:1pav>9h!s>9410r!

HONORSPRECALCULUS:UNIT7 NAME___________________________________DAY1NOTES:BEGINNINGTRIGONOMETRY DATE________________________PERIOD______TRIGON: METRON:I. REVIEWINGSINEANDCOSINEGRAPHS

Useyourknowledgeofbasictransformationstographthefollowing(LABELTHEAXESappropriately):1) 2)

3) 4) 5) 6)

2sin -= xy xy sin3-=

3cos += xy xy cos4=

xy cos-= 1sin2 += xy

Triangle measure

Iaia midlineo Gidtoo at a

vertical aFETEEiqo are ay

stretchgofink IfullPeriodI verticaly asin bx C td shift UBoorwn

r midline Vertical Shiftis 2 Down 2

I l I l l la E E t ea

0midlineup 3

EFFETE O

P I I l I lza in In Y I Tak Iz Iz'm2 2

Midline verticalstretchUp 1 of 2

iIH Iza 54in za Y tf i IaI IiiZ 2

Page 2: measure Iai - Weebly...%8q!!'=02!>1! yz[ \]^y \!u!!!!"""# $ %&"%'!, t%! ()! *+%!,-"*!. "$./%!"-)($_`*"(-g! o1!p>7!>70815!q410=a370 r!;asa7;!%f#t(!b737 u:1pav>9h!s>9410r!

II. REVIEW OF THE UNIT CIRCLE Last year, we explored the idea of finding heights and distances along the edge of a Ferris Wheel and looked specifically at a wheel with a radius of 1. We found out that when the radius = 1: sine represents ____________________________________. cosine represents __________________________________. If we were to plot the Ferris Wheel on a set of x- and y- axes, we would know all of the coordinates of the points shown. Fill in all degree values, radian values, heights, and displacements:

** The values for Quadrant I need to be committed to memory (for life… not crammed). There will be multiple quizzes on this beginning next class. Recall SohCahToa? sin V = cos V = tan V =

hypotenuseadjacent

oppositeθ

Y valuesTO

X values

sine sine cosinecosine NONE

i Fs 90 z

tl Fs

2 2 21 y TV3 2 ZFa Fa 3 3 4 WE Tz2 2 31 4 6 He 4 2 24 6120 60

53 I 5 74135 45 44 Ty TB 1Z Z 2 25 150 30 ke6

I O I 6,180 y 0 Oooo I 06 4 q 360 2K

4 I6Ty 210 330 Yet7 54 74 I6225 315 6

83 I B lz z

514

240 6h 300 774 2 Z

R2 R2 4 8 6 q513 r2 Tz

2 2 3 6 Z Zl Wz zig l FsZ Z 2 2

NONE O Cosinesine cosine sine

NTH

QA

Page 3: measure Iai - Weebly...%8q!!'=02!>1! yz[ \]^y \!u!!!!"""# $ %&"%'!, t%! ()! *+%!,-"*!. "$./%!"-)($_`*"(-g! o1!p>7!>70815!q410=a370 r!;asa7;!%f#t(!b737 u:1pav>9h!s>9410r!

Ex) What is YZ[ \]^Y \ ? III. REVIEW USE OF THE UNIT CIRCLE INFORMATION: Wecananswerquestions,givingEXACT(non-decimal)values,forquestionsinvolvingtheangleslistedontheunitcircle.

Ex:findtheexactvalueof(sin45°)(cos60°).

Ex2:Findtheexactvalueoftan60°.

Practice:(YouwillultimatelyneedtodothisonthetestWITHOUTbeinggiventhecircleandWITHOUTacalculator,soyoushouldfigureoutamethodforapproachingtheproblemswithoutanyresources!)

IV. ArcLengthReviewRecall:Acentralangle’sRADIANvaluewillequalitscorrespondingarc’sLENGTHwhentheradiusofthecircleis1unit.Thisisallrelatedtothefactthatthecircumferenceofacirclewithradiusof1unitwill=2π,andhenceafullcircleisdefinedtohaveananglemeasureof2πradians.So,howwillthearclengthchangeiftheradiusofthecircledoubles?Triples?Getscutinhalf?Writeaformulaforarclengthusingsforarclength,ɵfortheradianmeasureoftheangle,andrforradius.

tano

frae H FEITin 60 cos60 EE IF FI I

r

II

r15 2 bT 8T 7

cLength

g f IRadians

Page 4: measure Iai - Weebly...%8q!!'=02!>1! yz[ \]^y \!u!!!!"""# $ %&"%'!, t%! ()! *+%!,-"*!. "$./%!"-)($_`*"(-g! o1!p>7!>70815!q410=a370 r!;asa7;!%f#t(!b737 u:1pav>9h!s>9410r!

SECTORAREASupposeyouaretryingtofindtheareaofthesector(shadedregion).V = bcandd = 4.Findthearea,leavingyouranswerexact.Exploreusingothervaluesforthetaandr,leavingyouranswerforareaexact.Forexample,whatchangesifV = bf ?Takeyourfindingsanddevelopanareaformulaforsectors.Examples:Usethearclengthformulaandthegiveninformationtofindthemissingvariable.1. s=fbg ,r=2,θ=? 2.s=hhbf ,r=?,θ= biExamples:Usethesectorareaformulaandthegiveninformationtofindthemissingvariable.

1. A=?,r=3,θ=fbg 2.A=?,r=6,θ=bj

V. UnitConversionReviewHowdidweconvertbetweendegreesandradians?1.Convertkbl todegrees.2.Convert2.5radianstodegrees.

3.Convert67°toradians.4.Convert195°toradians.

radians

A YzQrZ Radius

F

roo452 21

0 4312.2

2 2 4 2 radians

O A zfr2YzL4 7135

4536

Degrees x geradians radians x Degrees

4 0615.3

0198047 670 6 radians