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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
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
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
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