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

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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