MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page1
Name:______________________________________________________________
TrigonometrySummerAssignmentDueDate:ThebeginningofclassonSeptember8,2017.
ThepurposeofthisassignmentistohaveyoupracticethemathematicalskillsnecessarytobesuccessfulinTrigonometry.AlloftheskillscoveredinthispacketarefromGeometry,Algebra1,andAlgebra2.Thematerialcoveredisfromourdistrictapproved,PearsonCommonCore,textbooks.Ifyouneedto,youmayusereferencematerialstorefreshyourmemory(oldnotes,textbooks,onlineresources,etc.).Whilegraphingcalculatorswillbeusedduringafewtestsandquizzes,themajorityofinclassassessmentsarenon-calculator.Youareencouragedtolearnhowtobecalculator-independent.Attheendofthispage,therearelinkstosomesuggestedonlinecalculators.
Trigonometryisafastpacedcoursethatistaughtatthecollegeleveltoprepareyouforcollegework.Thereisalotofmaterialinthecurriculumthatmustbecoveredbeforetheendoftheyear.Therefore,wecannotspendalotofclasstimere-teachingprerequisiteskills.Thisiswhyyouhavethispacket.SpendsometimewithitandmakesureyouareclearoneverythingcoveredinthispacketsothatyouwillbesuccessfulinTrigonometry.Ofcourse,youarealwayswelcomedtoseekhelpfromyourteacherifnecessary.
Thisassignmentwillbecollectedandgradedasyourfirsttest,thelastclassdayofthefirstweekofschool.Besuretoshowallappropriateworktosupportyouranswers.Inaddition,theremaybeaquizonthismaterialduringthefirstquarter.Allquestionsmustbecompletewiththecorrectwork.YoumustreturninSeptemberknowinghowtodoallthematerialinthispacket.
Forassistancewiththepacketyoumaycontactmeatgnaem@roselleschools.org.Emailsmaytakeafewdaysduringsummerforaresponse.Pleasebespecificinyouremailforwhatyouneedassistancewith,includethesectionandthequestionnumberaswell.Foreachquestioninthepacket,thereisanexampleintheseparatetutorialpacket.Thetutorialpacketispostedonlineonourschool’swebsite.Referencetopageandexamplenumbersislistedundereachquestion. CalculatorsLinksOnlineCalculator
https://www.desmos.com/calculator
https://mathway.com/graph
http://www.emathhelp.net/calculators/calculus-1/online-graphing-
calculator/
EmulatorforDownload
https://wabbit.codeplex.com/
http://lpg.ticalc.org/prj_tilem/download.html
GoodLuck!
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page2
1) Solvethefollowingproportions.
(TutorialPage2Example#1&2)a)About45ofevery300applespickedattheNewburyAppleOrchardarerotten.If3560appleswerepickedoneweek,abouthowmanyappleswererotten?
b)Theratioofthetwoacuteanglesinarighttriangleis5:13.Whatisthemeasureofeachangleintherighttriangle?
2) UsePythagoreanTheoremtosolve.
(TutorialPage3Example#1&2)a)Right∆ABChaslegsoflengths4ftand7ft.Whatisthelengthofthetriangle’shypotenuse?
b)Classifythetrianglewithsides7,9,and10asacute,right,orobtuse.
3) Usethediagramsbeloweachexercisetocompletea–b.
(TutorialPage4Example#1&2)a)Findthelengthofthelegofthetriangle.
b)Findthelengthofthehypotenuse,g,ofthetriangle.
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page3
4) Solvethefollowing.
(TutorialPage5Example#1&2)a)Findthevalueofttothenearesttenth.
b)Findm∠Mtothenearestdegree.
5) Findthevalueofx.Roundthelengthstothenearesttenthofaunit.
(TutorialPage6Example#1&2)a) b)
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page4
6) Usevectorstoanswerthefollowing.(TutorialPage7Example#1&2)
a)Describethedirectionofeachvector.
b)Findthemagnitudeofthegivenvectortothenearesttenth.
7) Findtheareaofeachgeometricshape.
(TutorialPage8Example#1&2)
a) b)
c)
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page5
8) Writethestandardequationofthecirclefromthegiveninformation.(TutorialPage9Example#1&2)
a)Center(2,−4);Point(6,−4) b)
9) Answerthefollowing:
(TutorialPage10Example#1&2)a)Findthecircumferenceofthecircle.Leaveyouranswersintermsofπ.
b)Findthelengthofarc UV! .Leaveyouranswersintermsofπ.
10) Findtheareasofcirclesandsectorsdescribedbelow.Writeyouranswerintermsofπandroundtothe
nearesttenth.(TutorialPage11Example#1&2)
a)Circlewithradius5. b)SectorABCincircleBofradius4and mAC! .
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page6
11) Solveeachequationfortheindicatedvariable.(TutorialPage12Example#1)
a) 2 5 1 , for3 12f g fg f+ = −
b) 3 4 , fora y a y yb− + = +
c) 3 ,4
x kj+ = forx
d) 12r+3s=1,forr
12) Solveeachinequality.Graphthesolution.
(TutorialPage13Example#1&2)a)4–(2x–4)≥5–(4x+3)
b)7–7(x–7)>–4+5x
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page7
13) Solveeachabsolutevalueequation.Checkyourwork.(TutorialPage14Example#1)
a) 2 3x − –4=3 b) 3 6x − +1=13
14) Completethestepstosolvetheinequality .
(TutorialPage14Example#2)
a) ≤ – 42x ≤ Rewriteasacompoundinequality.
b) ≤2x ≤ Addtoeachpart.
c) ≤ x ≤ Multiplyeachpartby .d)Whatisthesolution?
15) Evaluateeachfunctionforthegivenvalueofx,andwritetheinputandtheoutputasanorderedpair.
(TutorialPage7Example#3)a)h(x)=12xforx=4 b)t(x)=8x−5forx=7
4 32x − ≤
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page8
16) Writeanequationforeachline.(TutorialPage15Example#1)
a)m=4;contains(3,2) b)m=−1;contains(0,7)
c) d)
17) Grapheachequation.
(TutorialPage15Example#2)
a)−3x+2y=6 b)3y+x=3
c)2y−6=0 d)−2x+4y−3=0
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page9
18) Usingpoint-slopeform,writeanequationofthelinethrougheachpairofpoints.(TutorialPage16Example#1)
a)(−2,−5)and(8,−3) b)(3,5)and(0,7)
19) Writeanequationofeachlineinslope-interceptform.
(TutorialPage16Example#2&3)a)Through(−2,−2)andparalleltoy=−5x−4 b)Through(−4,1)andperpendiculartoy=−3x+7
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page10
20) Solveeachsystembygraphingorusingatable.Checkyouranswers.(TutorialPage17Example#1)
a)2 + + 3= 0 – 1 = x y
x y−⎧
⎨⎩
b) + = –2
–2 + 3 = –3x yx y
−⎧⎨⎩
21) Solveeachsystem.
(TutorialPage18Example#1&2)a)Solveeachsystembysubstitution.
–2 + = 6–7 + 6 = 1m nm n
⎧⎨⎩
b)Solveeachsystembyelimination.
5 + 4 = 6–2 – 3 = –1f mf m
⎧⎨⎩
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page11
22) Factoreachexpression.
(TutorialPage19Example#1&2)a)x2+6x+8
b)2x2−6x+4
c)9x2−6x+1
d)3x2+2x−8
e)27x2−12
f)16x2−32x+16
g)x2−64
h)125x2−100x+20
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page12
23) Solveeachequationbyfactoring.Checkyouranswers.
(TutorialPage20Example#1)a)x2−10x+16=0 b)2x2=−5x+12
c)2x2+10x=0 d)3x2−5x+2=0
24) Whatvaluecompletesthesquareforeachexpression?
(TutorialPage21Example#1)a)3x2+12x b)−7x2+14x
25) Rewriteeachequationinvertexform.
(TutorialPage21Example#2)a)y=x2+8x+13 c)y=2x2+4x−3
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page13
26) Whatarethesolutionsforeachequation?UsetheQuadraticFormula.
(TutorialPage22Example#1&2)a)−x2+7x−3=0 b)2x2+1=5−7x
27) Solveeachsystem.
(TutorialPage23Example#1&2)
a)2
2
62
y xy x
⎧ < − +⎪⎨
> −⎪⎩ b)
22 53 1
y x xy x
⎧ = − −⎨
= +⎩
28) Whatistheclassificationofeachpolynomialbyitsdegree?Byitsnumberofterms?Whatisitsend
behavior?(TutorialPage24Example#1)
a)8−6x3+3x+x3−2 b)15x7−7
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page14
29) Findthereal-numberrootsofeachradicalexpression.
(TutorialPage25Example#1)
a) 138
− b) 4 0.0001−
30) Simplifyeachradicalexpression.Useabsolutevaluesymbolswhenneeded.
(TutorialPage25Example#2)a) −x3 y63
b) 13313 3x
31) Simplifyeachproduct.
(TutorialPage26Example#1)
a) 2 5 23 336 6x y x y⋅ − b) 5 2 2 53 39 2x y x y− ⋅
32) Rationalizethedenominatorofeachexpression.Assumethatallvariablesarepositive.
(TutorialPage26Example#2)
a)21934
a babc
b)4 94yx
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page15
33) Simplify.
(TutorialPage27Example#1)a) 6 3 75− b) 3 3 38 3 24 192x x x− +
34) Simplify.Rationalizealldenominators.
(TutorialPage27Example#2)a) (4 6 1)( 6 4)− + b) 2 7
2 7−+
35) Simplifyeachexpression.Assumethatallvariablesarepositive.
(TutorialPage28Example#1&2)a)
1134(2 )(3 )y y b)
1 26 6( 3 )(7 )x x−
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page16
36) Writeeachexpressioninsimplestform.Assumethatallvariablesarepositive.(TutorialPage28Example#3)
a)
12416
825
z
x
−
⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠
b)
25
10
12
x
y
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠
37) Solve.Checkyoursolutions.
(TutorialPage29Example#1)a) 3 2 2 3x− − = b) 3 5 2 3 0x + − =
38) Solve.Checkforextraneoussolutions.
(TutorialPage29Example#2)a) 2 10 5x x− = − b) 1 7x x− + =
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page17
39) Letf(x)=4x−3andg(x)=x2+2.Performeachfunctionoperationandthenfindthedomainoftheresult.(TutorialPage30Example#1&2)
a)(f·g)(x) b)(f−g)(x)
c)f(g(2)) d)f(g(−5))
40) Findtheinverseofeachfunction.
(TutorialPage31Example#1)a) ( ) 2f x x= + b)f(x)=x+3
41) Namethedomainandrangeoftheinverseofthefunction.
(TutorialPage31Example#2)a) 5y x= + b) 3 2y x= +
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page18
42) Simplifyeachrationalexpression.Stateanyrestrictionsonthevariable.
(TutorialPage32Example#1)
a)2
2
+ + 2x xx x
b)2
2
3 126
xx x
−− −
43) Divide.Stateanyrestrictionsonthevariables.
(TutorialPage33Example#2)
a)2
2
3 12 8 16 2 8 8 16x x xx x x+ + +÷− − +
b)24 16 2 8
4 3 6x x xx x− − −÷
+
44) Assumethatthepolynomialsgivenarethedenominatorsofrationalexpressions.FindtheLCDofeach
set.(TutorialPage34Example#1)
a)x2+7x+12andx+4 b)x2–9andx2+2x–3
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page19
45) Simplifyeachsumordifference.Stateanyrestrictionsonthevariable.(TutorialPage34Example#2)
a) 2 2
25 6 3 2x
x x x x−
+ + + + b) 2
3 2 +
2 x 4x + −
46) Solveeachequation.Checkthesolutions.
(TutorialPage35Example#1)
a) 2
2 6 6–1x x x x
+ =−
b) 4 5 21 1x x= +
− −
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page20
47) Findthecenterandradiusofeachcircle.
(TutorialPage36Example#1)a)x2+y2+2x–6y=15 b)x2+y2–10x–4y=–20
48) Writeeachmeasureinradiansandcheck.
(TutorialPage37Example#1)a)150° b)45°
49) Writeeachmeasureindegreesandcheck.
(TutorialPage37Example#1)
a) 76π− b) 5
3π
50) Themeasureθofanangleinstandardpositionisgiven.Findtheexactvaluesofcosθandsinθfor
eachanglemeasure.(TutorialPage37Example#2)
a) 3 radians4π b) 2 radians
3π−
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page21
51) Usetheunitcircletocompletethefollowingtable.(TutorialPage38&39)
a)
θ in Degrees (Radians) Cosθ Sinθ Quadrant
0°
30°
45°
60°
90°
120°
135°
150°
180°
210°
225°
240°
270°
300°
315°
330°
360°
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page22
52) Findtheamplitudeandperiodofeachsinefunction.(TutorialPage40Example#1)
a) 1 sin 32
y θ= b) 44sin3
y πθ=
53) Grapheachfunction.
(TutorialPage40Example#2)
a) 12sin2
y θ= − b) 1 sin4
y θ= −
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page23
54) Sketchthegraphofeachfunctionintheintervalfrom0to2π.(TutorialPage41Example#1)
a) 1cos4
y πθ= b) 1cos22
y θ=
55) Findtheperiodandtwoasymptotesofthegraphofeachtangentfunction.Thenfindtwopointsoneach
graphthatarenotonthex-axis.(TutorialPage42Example#1)
a)y=4tanθ b)y=−tan2θ
56) Graphatleastthreecyclesofeachtangentfunction.
(TutorialPage43Example#2)a)y=3tanθ b)y=−2tan4θ
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page24
57) Determinetheamplitude,period,andanyphaseshiftorverticalshiftinthegraphsofthefunctions.
(TutorialPage44Example#1)
a) 2 sin( 3 )3
y x π π= + − b) 3cos 124
y x π⎛ ⎞= − + +⎜ ⎟⎝ ⎠
58) Sketcheachgraphintheintervalfrom0to2π.
(TutorialPage44Example#2)
a) 12sin 12
y x= − − b) y = cos3 x + π
2⎛⎝⎜
⎞⎠⎟+1
59) Findtheexactvalueofeachexpression.Donotuseacalculator.
(TutorialPage45Example#1)
a) sec − 3π
4⎛⎝⎜
⎞⎠⎟ b)
csc −
π2
⎛⎝⎜
⎞⎠⎟
MATHACHSTRIGONOMETRYSUMMERASSIGNMENTJUNE,2017Page25
60) Sketcheachgraphintheintervalfrom0to2π.
(TutorialPage45Example#2)a)y=−sec2θ b)y=cot3θ