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# Practice Final Exam Review MATH 113

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This 49 page Study Guide was uploaded by Katelynn Jones on Tuesday November 24, 2015. The Study Guide belongs to MATH 113 at University of Alabama - Tuscaloosa taught by Phylisicia carter in Fall 2015. Since its upload, it has received 34 views. For similar materials see - Precalculus Trigonometry in Mathematics (M) at University of Alabama - Tuscaloosa.

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Date Created: 11/24/15

1 Student Date 39 imam lawman an Nathan regiment mam anquot Jackson Tracy Elliott 1 Time 7 Course Ponta Math 113 TTR a 04amp05 Book Blitzer Algebra amp Trigonometry 5e Find the radian measure of the central angle of a circle of radius r 1 meter that intercepts an arc of length 5 1400 centimeters 39 v The radian measure of the central angle is Type an integer er a simpli ed freshen Convert the angle in radians to degrees e121 radians V 39 12 radians Convert the angle in degrees to radians Bound to two decnnalhplaces Find the length of the are s on a circle of radius r intercepted by a central angle 9 Express arc length in terms of 1 Then round your answer to two decimal places Radius r 17 feet Central angle 9 325 s Lj feet L Simplify year answer Type yon answer in ms of 1 expression I39 39 3 39 se integers or fraetlens fer any numbers the 393 w s feet 39 Type yarn answer mended to two decimal places Page 1 Histrident r r r W 7 gt I Instructof 113 ma a Aurora Poota Nathan ASSignment Prentice Exam Date 7 7 Jackson Tracy Elliott Time 77 Course Ponta Math 113 TTR 048505 Book Biitzer Algebra amp Trigogomeuy 5e Em Find the vertex focus and direetrix of the parabola with the given equation x 4220y3 vertex 3 4 foetus 39 directrix y 1 vertex 43 focus 4 2 direeu39ix X 8 vertex 43 focus 48 directrix y 2 QB vertex 43 30 focus 42 7 2 direotrix y e 8 7 7quot Page 36 Course Ponta Math asgr maquot391391mg maggisg ta 135 Essig m eatf iagiiee Fmi Egam Jackson Tracy Elliott 113 TTR 048505 BmlgfiB tzen Alggbra amp Trigunom tty 5t 7 r r I Use the Pythagorean Theorem to nd the length of the B missing side of the right triangle Then nd the value 39 of each of the six trigonometric mctions of B The length of the n ssingsidg 116 right triangle is a 3 Y ur answ r i113 expressigm cns t I YGIH MSWEI inchi jnquot g fa jg 3 expressia ta Simplify yemi m ar radicais amassing csc x yam answer radical expression sec 9 Simp fy yen mar any radicals cote E S np fy your war any mdicaals expressian U55 integefs r actians f0 any numbers 13921 the c26v Tl Usc integars m fragam fer numbers in the Use integers r actims far any nmnbers in the Use intng 31 atti s far 3113 numbers in tha Use a actians far any numbem in 113 Use iategers 0r a timzs far any the Find a co mction with the same value as the given expression cos 27 sin 63 78 sec 27 c39f 1 C 86 63 79 sin 27 Page 2 Stndent Date Jackson Tracy Elliott Course Ponta Math 113 TR a 04amp05 39 Time EM 1 32 7533 Book Blitzer Algebra amp Trigonometry Se Find the vertex focus and direenix of the parabola with the given equation Then graph the parabola x32 4y 3 The vertex of the parabola is 39 a Tweenordered pair 3 i 5 39 The fecus of the parabola is I r 1quot an ordered pair The directrix of the parabola is a J Type an aqua 39 8amp3ny 3mm aeswt r Instructor 113 math Aurora Ponta Nathan Assignment Practice F Exam Use the gTaPhing tool to graph the parabola I fw lt 39 mink to emerge I Find the focus and directrix of the parabola with the given equation x2 16y a focus 0 4 a directrix y quot 4 quot 8 focus 04 directrix y m quot4 theme 0 m 4 directrix y 4 SD focus 80 directrix x i 4 13 Convert the equation to the standard fem for a parabola by completing the square on x or y as appropriate y2w4y6x200 wet y 22 6X4 ec y 22 lax 4 y226x 4 Page 35 6X4 f Student 3 Date imam N133 5511 A ior puma Nadia Ass g t mega Final Em Jackson Tracy Elliott Time Course Ponta Math 1 13 TTR 048105 fa Book Blitzer Algebra amp Trigonometry Se 7 Use identities to find the exact value of each of the four remaining trigonometric mctions of the acute angle 8 1 sin8 5 Simplify yoi ESWiBI zadieaiigx Use integers or eetioms for any numbers the expxeesiom 739 amp Simpli i yourimwer algaljediggig Lise inte ers or fractions for any nominee39s the expression sec Di i Simplify yout eoswer iecluditige y integers or eetioes for any numbers in the expressiom I L I Shoplify your answer inch my radicals Use integers or aetions for my numbers in the expression Use a calculator to nd the approxilnate value of the expression Round to two decimal places sin 64 m fie 098 QB 100 390 092 To nd the distance across a lake 3 solveyer took the measurements in the gure shown Use these measurements to detemine how far it is across the lake Round the ewe to the nearest whoie number Page 3 stings quot 39 7 39 quot WinstruetoiiliS niath Am Ponta man Assignment Practice Final Em 39 fDate 7 Jackson Tracy Elliott 3 Time 7 Course Ponta Math 113 TTR 048505 7 7 7 BWRSBHWWECW 5 Worm 7 91 Find the standard form of the equation of the hyperbole satisfying the given Conditions Center 5 e 6 focus 10 6 vertex 9 6 The equation is 39 e 1 standard form of the equation Of The form of equation I hyperbole shown below n tee we got Find an equation for the hyperboia whose graph is The Standard fom 0f the equation is below 43 39 4 i 39 e we Find the standard form of the equation of the parabola satisfying the given conditions Focus 130 Directtix X 13 The standard form of the equation is Type an equation Simplify yoox answer Page 34 men 7 39 Date gt ensignment N Jacksom Tracy Elliott Course Ponta Math 113 HR 048565 Time it El 12 Book Blitzer Algebra amp Trigonometry 5e Find values of the nigonomet e functions of the angle in standard pnsition Whose terminal side passes through the given point Simplify answer ineluding ragieal integeg frs er aetiene fer any numbers the expreeeien cot 6 h E Simplify yew answer including sec 9 Snnplify year ans er inelnding Use integers er aetinne fer any numbers in the exnressienj cchxL J quot n Simplify you answer ineln img Use integers or aetiene fer anr numbers in the expreeeien A point 011 the terminal side of angle 6 is given Find the exact value of the indicated trigonometric mction of 3 w 2048 Find sin e 13 13 Find the reference angle for the angle 65 5 The reference angle is U D Page 4 Student 39 39 Date quotmeager1 1393 manger pom em migheegm ce Em 39 Jackson Tracy Elliott i Time Course Ponta Math 113 TTR 04amp65 3995 95 Book Blitzer Algebra amp Trigonometry 5e Convert the equation to the Standard form for an ellipse by completing the square on x and y r 39139 3 3 an 5 r y 393 2 2 2 M JL X 7 Y 1 a H 3 2 2 2 the x 7 y 1 25 15 I 251 E 1 8 Find the vertices and locate the foci of the hyperbola with the given equation Then graph the equation 139 The vertiees of the hyperbole are f E Type an ordereo pair Simp fy your USEj iquot39 EEim hequotto aetneeewgz 7 7 w W n The foei are located at H p J Type en ordered Simplify your weroype an exact answer radicals as nee ied Use a com to separate answers as needeti Choose the correct graph below Find the stande form of the equation of the hyperbole satisfying the given conditions Foei at 0 m 3 and 03 vertices at 01 and G I The equation is Page 33 seas 39 quot quot imagequot as math Am Ponta Namngggnmaa manna 39 397 39 11 Date Jackson Tracy Elliott 5 Time Course Ponta Math 113 TTR D4amp05 Book Blitzer Algebra amp T genometry 5e 7 W 92 Graph the ellipse and give the location of its feci 2 2 x 3 r 9 16 Choose the correct graph below A 533 in firm I Fail 3 33quot H f quotVs 7 The face are located at rr L 7 2 39 39 a a T ordered a eemma tn separate as needed year an exact mwer using radicals as needed s3w Find the standard form of the equation of the ellipse satisfying the given canditions Major axis horizontal with length 10 length of minor axis 4 center 00 Page 32 39Siu39deiit Date Iiistructor 1i3 math Aurora Ponta Nathan Aesignment Final Jackson Tracy Elliott Course Ponta Math 113 1111 04amp05 39 Time 23 M iii Book Blitzer Algebra amp Trigonometry 5e Use reference angles to nd the exact value of the expression Do not use a calculator sin 765 I as E 2 E5 1 2 if 2 2 The point Pxy on the unit circle that eorresponds to a real number t is given Find the values of the indicated trigonometric function at t Find see L 4 4 39 3 15 13 we Let sin t a cos it b and tan t 3 Write the expression in tenths of a b and 6 sin t 10a v cos tl 2n tan t 911 sin t 1075 j cos If 21 tan tee 97 Simpii r your lquot i as xquot 39 39339 Test i 2 3 3 33 7 7 7quot Page 5 vanes Date Instructors 113 Aurora Fonts Nathan Assignment PtaeticeFinal I Jackson Tracy Elliott Time Course Ponta Math 113 TTR 048005 39 91 Book Blitzer Algebra amp Trigonometry 5e A person is pulling a freight cart with a force of 53 pounds How much work is done in moving the cart 60 feet if the cart s handle makes an angle of 20 with the ground Round your answer to the nearest tenth 29882 ft lb agjis 1088 ib 10876 l b TED 30716 ft lb Graph the ellipse and locate the foei 2 2 x I i 1 81 25 Choose the correct graph below M f B La 3 D 9st sit L itquot 43 m2 Loeage tminpi 7 T 7e ordered Use a answers Type exact were using radicals as needed Simplify your answers Find the standard form of the equation of the ellipse and give the location of its eff foei The standard form of the equation of the ellipse is 1 The foei are located at it 1quot ype ordered pairs Use a comma to separate answers as needed your answers an exact answer using radicals as needed Page 31 settle 39 397 f Date 39 inletaerial 3 math Accelerator newt rimLee Fine 3 quot 39 397 397 39 Jackson Tracy Elliott Course Ponta Math 113 TTR 048505 Time 3 l3 Book Blitzer Algebra 8r I gonome y 5e Use periodic properties of the trigonometric functions to nd the exact value of the expression tanm39 g 1 QB 1 ftSC 3 GD V3 Select the correct choice below and ll in any 7 711 Use the unit c1rc1e to nd the value of tan 4 and answer boxes in your Choicei h periodic properties of trigonometric mctions to nd I x 27 quotit 7 the value of tan f an exact answer using redlcglieiee needed Simplify your answer Rationalize in the deeominator iiquot 7 PW itquot i 2 i 2 I 4 B The solution 13 unde ned QT c 4quot4 zjoj quot X Select the correct choice below and llinftny answer boxes in your choice 772 quot Type an exact answer using redicale as oeetlecl your Rationalize the eerietor 533 The solution is unde ned Let sin t a cost t b and tan t c Write the expression in terms of a b and c 8 sin d t w sint 8 Sin t Sill t Simpli f your answer to t1 an 5 39 if 1 Page 6 asmden t I u 7 I Instruci fl 113 math Aux fa As ign i n ra tice H H 5 Date Jackson Tracy Elliott Time 7 Course Ponta Math 113 TTR 048505 Bunk Blitzcr Algebra amp Trigonometry 5e 1g Detem ne the amplitude period and phase shift if 4 at any of the given function Graph the mction f 1amp5 51 E w 39 1 g y 5 sm 2 gins 3 z 1 J y 51 251 g gt 6212 f The amplitude is 82 67 23 Simplify yam answer Type an exact answera aging as matted 7 4 The period is n 3975 Sp fy your answar Type an 3 as named The phase shift is 310m answer Type an exact answari usng 2 as needed Use the graphing tool to graph the flmction i can in 9 aniarge u 3 g Fm any answer boxes Shawn with the grapheer type an exam Type the worci pi t0 the symbol 5 as naedad Page 7 Student Date I 39Inetruetort 113 math Aurora l onta Nathon Assignment Practice V V Jackson Tracy Elliott Time Course Ponta Math 113 04amp05 85 35 S7 83 Book Blitzer Algebra iv Trigonometry 5e The gure shows a box being pulled up a ramp inclined at 21o from the horizontal E Use the following information to solve the problem 2137quot r E 2 force of gravity t weight 0f the box quot p magnitude of the force needed to pull the box up the r ACEmm lw magnitude of the force of the box against the ramp If a force of 20 pounds is needed to pull the box up the ramp nd the weight of the box Arutlquot may The weight of the box is approximately pounds Type an integer or decimal rounded to the nearest tentn39neneeded Given V 7i 8j and w 3i 4j nd the following avw a v i1 I b v v Use the dot product to determine whether v and W are orthogonal vz3i3jw 2i2j Are vectors v and w orthogonal Find the angle between the given vectors Round to the nearest tenth of a degree ui jv5i61 JH I l I O 97 4 l ec 952 quot1e 1 Page 30 Date Time 3 3i 3 1 Student Instructor 113 math Aurora Ponta Nathan Assignment Practice Final Exam Jaeksom Tracy Elliott Course Ponta Math 113 TTR 043505 Book Blitzer Algebra 8 Trigonometry 5e Find all the complex square roots of W Z 64 cos 60 i sin 60quot Write the roots in polar form with 6 in degrees quot 7 i r a r 39 30 UMSD i v ype answers degrees Retrial to 39 21 UCOSDD i J Type answers in degrees Reund he the e Hist image Let v be the vector orn initial point P1 to terminal point P3 Write v in terms of i and j Pjie3 LP2f amp 9 v Type your answer in terms at i and 3 Let 11 4i 4j and v e 5i Sj Find the vector uv u v Simplify your answer Type freer answer in terms ef i and j One rape pulls a barge directly east with a force of 44 newtons and another rope pulls the barge directly north with a force of 45 newtons Find the magnitude of the resultant force acting on the barge Round t0 the nearest whole number FA lneMons 23938 1980 newtons 63 newtons D 89 newtons Find the unit vector that has the same direction as the Veetor v gt i v HHH y gw39d 1 5 i The unit vector that has the same direction as the vector v is Shapiify your merger irisladng any radiealst Use integers er fractions for are in the expressiea Type your answer in teens of i and 3 Write the vector v in terms of i and j Whose magnitude v II and direction angle 6 are given Ilvli2s 9240 h r I l 39 o 2 yquot g I r V I it A Liv 7 Km 1 k Simplify your answer including any EUse integerser fer the 39erpfessiee Page 29 magi 39 Date Jacksan Tracy Elliott Course Ponta Math 113 HR 048505 39 Time 2 521 Book Blitzex Algebra Trigonom tly 56 r J 7 Determine the amplitude period and phase shift of the mction Then graph the function y sin 42 27 4 The amplitude isEl 7 i The period is 9 2 a Type an amt answ using naei f se 125 39 miegers m agtians for any Rumbas in the axpressionj 4giam V T The phase shift is lj Gym an exact answer 153mg is g I 5139 quot quot 39 integars gr ac39tians far all numbeis in the 7 39 quotI f 3 39 exprexion Use the graphing tool to graph the function Gimme Brim g9 gram 39323 Shawn with tbs grapher type an arms answer Typa the W611i pi in insert the symhei 1 as waded Determine the phase shift of the function 4 2 I 5 3111 x F39 y 2 HA 21m units down 75 93 1 units to the right 395 TE 5 units to the le 4n unitsup Page 8 sampucfor A cr Pd tmNa l nm ssignment Exam 7 V I i Studerlt d Date 113 math Aurora Poeta Nathan Assignment melee Final Jackson Tracy Elliott i Time Course Ponta Math 113 TTR 048505 35 quot3 6 71 Book Blitzer Algebra 8 Trigonometry 5e Write the complex number in rectangular form I 3 cos 210 i sin 210 your aneweri including any radicals or asay it the expressioe Ra ona ze all denommatorsi Type your answers in the form e 131 Find zw Leave your answer in polar form I 39 9 39m 397 n quotquot Zquot ms 10 15mm 3 n 7quot quot we rtes 1 1 1 11 7 I Jr i Red ce any freedom Describe the angle 113mg radians between E and 22L Z 7 Find the quotient 1 of the complex numbers Leave your answer in polar form 32 21Z4ees 12 r sin12 226c0540t i sin4 Choose the correct answer below r L W a 7 l 3M4 2A 4cos 3 i sin 3 3 4 cos 8 i sin8 4cos 12 c0540 Si 120 Sin4o quot JD 4e0512quot sin 4 i sin 12 cos 4 Use DeMoine s Theorem to nd the indicated power of the complex number Write the answer in rectanglllarfonn e a quot 4cos110 i sin 110 3 4 cos 110 139 sin 110 3 7quot 7 Simplify your answer including any radicals Type your answer in the form a bi Use integere or fractions for any embers in the expression Re ona ze the denominator Page 28 image E Date illistrlictori 113 math Autoea P onta Nathan Assign lelit Practice Jackson Traey Elliott Time Course Ponta Math 113 TTR 048505 2 23 Detemu39ne the amplitude and period of the following equot Book Blitzer Algebra amp T gonometry 5e tits 5 inetion Then graph the mction we 1 9 The amplitude is QR 7 2 The period is D t 39 r Type an exact answer rising it as integers or eetions for any embers in the expreseionm 5 a i E qg 7 5e E Use the graphing tool to graph the function r eiieem 5 emerge 39 39 j or any an bexes Shawn with the gmpher 139 I 3 39 expression an emet answer Type the ward pi to insert the M w h A 73 symbol a as needed Determine the amplitude period and phase shift of fe the function Then graph the mction y cos x it 4 The amplitude is l t 3 39 39 39 quot e Lee 1 at The period is 7 7 777 3 39 Type an exact using 7 a needed Use integers or fractions for any numbers in the 57 The phase shift is E i 7 Type an exact answera g asneeded Use f 39 39i 1 I E integers or eetions for any numbers in the i Qi ri39 expressioeg t 39 Use the graphing tool to graph the function seeker 7 Emma 1 emeh K boxes shown with the grapher type an exam answer the word pi te the symbel 2 as nee ed Page 9 Student 7 Instructor 113 math Aurora Ponta Nathan Assignment Practice Final Exam Date 77 Iaeksen Tracy Elliott Time 7 7 7 Course Puma Math 113 048505 Book Blitzer Algebra amp Trigonometry 5e 3 Plot the complex number and nd its absolute value 2 5 5 139 First plot the complex number 2 H 5 5 i 2A B magma 3 iii g axle l i i I eels axle fa g l i 3 lm o Miguel Lumen Find the absolute value Izl l SeSilZE Type an exact answer using simpli ed radicals as nee ed E4 Plot the complex number then write the complex number in polar form You may express the argument in degrees 3 3V3 139 Choose the correct graph of the complex number 3A e be 4 i 39 e e gt a 3 all H mm 42 PU E x m j e Ci HITIL L z integers fer y n bets in the expressien Page 27 t aen f Date Jackson Tracy Elliott 1 Time 7 7 Course Ponta Math 113 TTR O4amp05 223 ES 26 Book Blitzer Algebra amp T gonomooyo re Use a vertical shift to graph the function 4 1 z 2 X l E not L y Egg 55 3 EB 12 2 if L x iii Graph two periods of the giveiiafiin ent fu ction y H 2 tan ix Choose the correct graph of two periods of y m 2 tan below Graph two periods of the given cotangent mction l t3 y 5 on X 1 Choose the correct graph of two periods of y cot 31 below A j a c 4 a i quot A 2 s i 4 j 4 i 15 El j i bm s1 h39fT go has A Wiiiltll iiii M LLWLLJ Page 391 0 mamas 13 amga 1m mo Agoogo Praotico FiiiaiExam 39 3 Student 7 H 7 i I Instructor 7113 math Aurora Ponta Nathan Aesignoieol Practice Exam Date 7 7 Jackson Tracy Elliott Time 7 7 Course Ponta Math 113 TTR 04amp05 Book Blitzer Algebra Sc Trigonometry 5e 31 Convert the polar equation to a rectangular equation Then use a rectangular coordinate system to graph the rectangular equation r 3 use 9 The rectangular equation for r 3 use 6 is Type an equation Choose the correct graph of the rectangular equation below e e39 it W 1 M 51 hr ee g re 11 Convert the rectangular equation to a polar equation that expresses r in terms of 9 2x 3y 12 0 m 12 r t 2 cosB S siriB QB 2 3033 3 sin 9 quot 12 12 h 2 Sill 3 cos ED 2 cos 6 3 sin 9 12 Page 26 5 Strident Date if math Ponta Natheh Aosignment Practice Exam Jackson Tracy Elliott Time Course P011123 Math 113 TTR i 048505 3 23 Book Blitzer Aigebra amp Trigonometry Se Use the following graph to obtain the graph of the What is the equation of the reciprocal lnction Figg hM goa39xquot 1 we function found by replacing sin with its reciprocal metion Give the equation of the function for the y M quot gtr graph that You obtam Type ahe ee39siioh as the variable Use 31 integers or fractions for any embers in re ii expression V sin 3 Choose the correct graph below 4 Graph two periods of the given secant function y 3 sec 3x Choose the correct graph below W m quot 39quotlt Page 11 1 some W 7 39 39 Date I Inmate 7 71713 math we Puma Nathan I regime Final Ei ni Jackson Tracy Elliott 7 Time Course Ponta Math 113 048505 6 38 6 3 9 Two points A and B are on opposite sides of a building A surveyor selects a third point C to place a transit Book Blitzer Algebra amp Trigonometry 5e 77 N quot Point C is 51 feet from point A and 67 feet om point B The angle ACE is 54 How far apart are pointswgw a 39 quot 554 feet E I 954 feet I J 39 u quot 39 39 i 1054 feet 39 quot I WW3 39ff D 713 feet The polar coordinates of a point are given Find the rectangular coordinates of this point f K Le 5 4 at 39 t a What are the rectangular coordinates of this point L a EV ii 941 5 39 e 17 3 quotl i n l 31 r 1 Type an orifeed your answer inelo ing any radicals Use integers or Erecting for any numbers in the expreesion The rectangular coordinates of a point Megymr5mdwlm coordinates of the point such 139 gt 0 and 39 j g39 o l Ewenr m 6 7239 The polar coordinates are f i f 3 a E 39 is Type an orderefi Joan Type your Type an exact I your amen Convert the rectangular equation totapolanequationi xpres s r in terms of 8 t t 7H 7 i 4xy7 rzzLi Type an exact answer 39 Page 25 113 math Aurore Ponta Nathan Assignment Practice Exam isms f Date 7 7 77 Jackson Tracy Elliott Time 7 Course Ponta Math 113 39ITR 048505 r Book B tzer Algebraamp Trigonometry Se 7 W 7 r N r 29 Find the exact value of the expression m 711 2 l 1 cos 39 Type yes answ iadians Type an exact using quotIE needed Else ietegers er actions for any numbers the expression 33 Find the exact value of the expression tan 1 quot 39 J 3 3 3 32 Find the exact value of the following expression possible Do not use a calculator 1 57r V I I I i 311 Sin quot i quot 6 I 7 7 Select the correct choice below and if necessary ll in the answer box to complete your choice CA 1 57 5111 111 We 6 Type an exact ense rerg as needed Type an integer er a simpli ed eetion 33 The expression is unde ned Page 12 Student W 7 7 739 Ins h tor 113 math Aurelia pm Na xanwgs sig meni Practice Exam Date 7 Jackson Tracy Elliott Time Course Puma Math 113 TTR 048505 r 7 Book Blitzex Algebra amp Trigonometxy Se 33 Find the exact value of the expression if passible Do not use a calculator cos cos w 39 575 6 7139 6 q 71 u 6 3 7 7quot 39 6 323 Use a sketch to nd the exact valua of the expression ms 51 5 W an m 2 39 n 3 5 z 3 5 39 5 h 1 5 Page 13 seen Date Jackson Tracy Elliott Ceurse Ponta Math 113 TTR 048505 Time 63 465 Book BlitZer Algebra 8 Trigonometry Se 39 new 113 naequot Aurore mamas memes PmetieeFinat Exam A surveyor standing 53 meters from the base of a building measures the angle to the top of the building and nds it to be 37 The surveyor then measures the angle to the top of the radio tower on the building and nds that it is 48 How is the radio tower 31113 1030 meters 2 t 749 meters 51C 686 meters 1892 meters Solve the triangle 1 1 c 3 A 2 140 7 5 5 7 E 1 r 5 a g x u 1 1 De net mend until the nal answer Then round t0 the nearest teeth as B a D 0 quot Be not rennet anti the nal answer Then mend te the nearest degree as needed can De net round the mswer Then mend te the nearest deee as needeti Solve the triangle 364b24 c47 De net round the nal answer Then re ne the nearest degree as needed A golfer hits an errant tee shot that lands in the rough A marker in the center of the fairway is 150 yards from the center of the green While standing on the marker and facing the green the golfer turns 125 towards his ball He then paces off 30 yards to his ball How far is the ball from the center of the green The ball is about yards from the center of the green Reuntt to one place as neetied Page 24 lseydf marker Ra hm r 5 ffstud st 39 39 399 Date 7 Time Instrnctor 711339 math legs so Nathan Assiigsinent peers the exam Jackson Tracy Elliott Course Ponta Math 113 39ITR 048505 6t 61 62 Book Bh39tzer Algebra 85 Trigonometry Se Two sides and an angle SSA of a triangle are given Determine whether the given measurements produce one triangle two triangles or no triangle at all Solve each triangle that results 310 b3 A60 3 4 Selected the correct choice below and if necessary ll in the answer boxes to complete your choice as Round side lengths to the nearest tenth and angle measurements to the nearest degree as needed There is only one possible solution for the triangle 7 I I The measurements for the remaining side 6 and angles B and C are as follows 5 There are two possible solutions for the triangle f The measurements for the solution with the the smaller angle B are as follows i quot33 39 39 Bl W f xiii C 61 e f The measurements for the solution with the the larger angle B are as follows E quotquotquotquotquot i 39 CZWUO If 3 w 39 l1 There are no possible solutions for this triangle Find the area of the triangle having the given measurements C 125 a 5 meters 13 E 4 meters A re square meters Round the answer to the nearest square unit i ar s 1 7 3 M 7 t Two sides and an angle S SA of a triangle are given Determine whether the given measurements produce one triangle two triangles or no triangle at all Solve each triangle that results Round lengths to the nearest tenth and angle measmes to the nearest degree lt 32 A 2 30 3 12 b a 24 a EB no triangle B 900 C 60quot c 208 B 60 C 60 c 208 B 60 C 90 01208 Page 23 Li smaeigtz77 39 7 739 7 77 7 7 77 quot 7 7 iii iietar 77iifa as Aura Ponta ma Mm Practiee anal Emu 7 7 77 Date Jackson Tracy Elliott i Time Course Ponta Math 113 TTR 048205 3 Book Blitzer Algebra amp Trigonometry 5e Use substitution to determine whether the given x value is a solution of the equation 27 tan3x P 1 11 211 1 x IS a solutlon of the equation 2W all x 9 is not a solution of the equatmn 53 Find all solutions of the equation 5cosx5 3 cosx4V 1 117 X i 2117 or X 2117 6 6 7 51 3977 8 Xz g 2 OIX 6 2 7 if 111 JC x 1 mt or x 111 6 6 57 77 x 117 or x na 6 6 Solve the triangle ftp W BI1 Do not round until the nal answer Tli ii to the nearest degree as needed I L r I 39 39 1 h 39 k 39 t V I V 5 Do not round until the nal answer Then round to the nearest teeth as merited 39 r i g 3 39 i 39 gr V 7 u 4 quotquot 39 39 r 39 z 7 Q r 39Fz39 1 y r Do not round until the nal Then retold to the nearest tenth as needed Page 22 scam 39 H quota quot Date Jackson Tracy Elliott 1 Time 7 77 Course Ponta Math 113 TTR a 04amp05 V Instructor 113 math Aurora Ponta Nathan Assignment Practice Final Exam Book Blitzer Algebra 8 Trigonometry 5e 54 Solve the equation over the interval 02a 39 e 39 V cos 2 ii 2 r I I Select the correct choice below and if necessary ll in the answer box to complete your choice Type exact answers in terms of it Use integers or actions for any numbers in the expressions Use a comma to separate answers as needed VB There is no solution 55 Solve the equation on the interval 0 21 2sin26 sinliw10 What is the solution in the interval 0 2a Select the correct choice and ll in any answer boxes in your choice below fo 3 Simplify answer Type an exact answer using a as needed Type your answer in Use integers or actions for any in the expression Use a comma to separate as needed iifia B There is no solution 56 Solve the following equation on the interval 0210 sinx Zsinxcosx0 Select the correct choice below and if necessary ll in the answer box to complete your choice Type an exact answer a as needed Use a comma to separate answers as needed Type your answer in radians Use integers or fractions for any numbers in the expressions quotEB There is no solution Page 21 5 Student instructor 113 math Aurora Ponta Nathan Assignment Practice Final Exam Date Jackson Tracy Elliott Time Course Ponta Math 113 TTR D4amp05 51 22 Book Blitzer Algebra 8 Trigonometry Se Write the following expression as the sine cosine or tangent of a doubleangle Then find the exact value of the expression 2 t It an itquot 1 w tan 2 6 Wha is the given expression equal to a 3139 tan 3 7 712 cos quot 3 n 39 cos 6 t W an 6 The exact value of the expression is i Type an exact answer using radicals as nee leti Rationaline the denominator Use a halfangle formula to nd the exact value of the expression tan 1125 1 39 g k 2le 1 B V i 1 1 CED 1 Use the gure to nd the exact value of the following trigonometric function a 7 Sin EL 2 a H 7 an 3 a Simplify your ansiner including any radicals Use integers or fractions for any numbers in the expression Page 20 3 Student 7 Instructor 113 math Aurora Ponta Nadian Assignment Practice Final Date W Jackson Tracy Elliott Time 7 Ceurse Ponta Math 113 TTR 04805 Book Blitzer Algebra amp Trigonometry 5e 48 Find the exact value of tan a 9 under the given conditions 29 it 15 712 sin n E 0 lt a lt 3 cos B Y7 0 lt 3 lt 511 11 New quotA 468 468 39 53 155 7 FWD 475 19 49 Use the gure to nd the exact value of the following trigonometric function cos 2a wmwmsegtquotquot39 cos 21 Simplify yen answer in Use the given infonnation to nd the exact value of each of the following f a sin 29 1 ms 29 0 tan 29 I sin9 g 9 lies in quadrant l39 a sin 29 D L l yew answer including integers or eeting 1113an in the expressinn b ms 29 3 D 91139 939 7 r 7 7 V Simplify your answer inninding any radicals Use integers er g gf f in the enpressiun c ten 29 l Simplify yen answer ineinding any radicals ii e integers of aetiens for any nuntherein the expreseie Page 19 Students 2 Date Instructor 7 113 niath Aurora Ponta Nathan Assignment Practice Final Exam Jackson Tracy Elliott Time Course Ponta Math 113 TTR 0482205 45 4 Book Blitzer Algebra amp Trigonometry 5e Write the expression as the sine cosine or tangent of an angle Then nd the exact value of the expression tan 20 tan 10D 1 tan 20 tan 10 39 Write the expression as the sine cosine or tangent of a single angle Do Find the exact value of the expression tan 20 tan 10 39 e an 1 tan 20 tan 10 Type an exact answer in fraction format using radicals as needed and rationalize any denominator tan 20 tan 10 1 tan 20 tan 10 Write the expression as the sine cosine or tangent of an angle Then nd the exact value of the expression sin cos 39 cos iquot sin 7 12 4 12 4 Write the expression as the sine cosine or tangent of a single angle 51 7t 57 a r sin cos cos sin 1 39 r 12 4 a a 12 4 Use integers or fractions for any numbers in the expression Simplify your answer Do not evaluate 5a 7 51 7 sin cos cos sin 12 4 12 4 W L Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for any numbers in the expression Rationalize all denominators Page 18 i V i r 77 7 Instructor 113 math Aurora Ponta Nathan assignment Practice I Date 7 Jackson Tracy Elliott Time 7 Course Ponta Math 113 TTR 043505 Book Blitzer Algebra 8 Trigonometry 5e 44 Write the expression as the sine cosine or tangent of an angle Then nd the exact value of the expression are39 L tan tan 3 t r j it a 1 tanr ta39n 5 30 Write the expression as the sine cosine or tangent of a single angle 7 7 tan e tan 30 1 7E 75 in LA 1 g i E tan tan w 5 30 Type an exact answer using a as needeti Use integers or aetions fer any nemesis in the expressien Find the exact value of the expression 1 n ta at an5 1130 Sitnpiify your answer Type an exact answer using ratiieais as needed Use integers or aetions for any numbers in the expression Rationalize all denominators 45 In the following problem the expression is the right side of the fonnula for eosu 3 with particular values for a and I3 ces98 20508quot sin98 sin38 3 Identify a and B in each expression The value for e 3 The value for B D I Write the expression as the cosine of an angle cos c Find the exact value of the expression Type an exaet answer using astion radieais and a rationalized denominator Page 17 395 Student Date Jackson Tracy Elliott Course Ponta Math 113 I TR 048505 Time 434 42 113 methj Foetal Nathan rn39lm ent Practice Final W W Book Blitzer Algebra amp Trigonometry 5e Rewrite the expression in terms of the given function 0r metions cos 2x cusx 1 sin 2x cosx cosx 28 2 cos x cosx JD 2 cesx t y Verify the identity sin el WP tane sect3 c033 Choose the sequence of steps below that veri es the identity 131A sin 1 sin 9 l t 8 6 quot an see cos 6 cos 9 cos B siftB sin 9 1 cos 9 cos 3 I r tan 8 secB quot cos 9 5m 8 l sinB 1 l sinEl t 8 B an sec cos 8 ms 9 cos 6 sin 9 1 sin 9 1 m E tan 8 sec 8 cos 9 cos 6 cos 6 Verify the identity cot 4t csc 4t 2cot 2t1 Which of the following four statements establishes the identity ytt cot 4t cse 4t csc 2t cot 2tw csc 2t 2 eat 2t 1 quot 3 cot 4t csc 41 cut 2t cot 2t csc 2t 2 wt 21 1 5 e Page 16 cot 4t w cse 4t cut 2I es 21 cot 2t csc 2t I e 2 cut 2t 1 cat 4t csc 4t not 21 csc 2t cot 212 esc 2t e 2 cat at e 1 student Date Jackson Tracy Elliott Time Course Ponta Math 113 TTR 048505 38 39 4 Book Blitzer Algebra amp Trigonometiy Se A boat leaves the entrance to a harbor and travels 100 miles on a bearing of N 55D E How many miles north and how many miles east from the harbor has the boat haveledg The boat has traveled miles north Reund m the nearest tenth of a mile The boat has traveled miles east Olequ he the nearest tenth 0f 3 mile Using the given gure nd the bearing from O to D A N 126 W 39jffaB N 1540 E S 54quot E QB S 54D W Complete the identity sin39x cos X 9 cos x sin x sec xcsc x 1 cotx 5 39C 2tan 2X D sin xtan X Page 15 Insiiilielor 113 math Ahrera Ponta Nathan Assignment Practice Final Exam Student 7 5 Date Assignment Practice I Jackson Tracy Elliott Course Ponta Math 113 z 043505 La U1 36 U J Solve the right triangle shown in the gure Beak Blitzer Algebra amp Trigonometry 5e A 1 595 c 56 a What are the lengths of the sides a e Reend m the nearest hundredth needed h z R fl to the nearest es eeeded b What are the eagles B to the nearest teeth as needetl C O Find the length X to the nearest whole number X z ii 5 39 39 i De net the nal answer mend te e L quotE 39 the newest Whole number ham 37 500 24 g The Statue of Liberty is approximater 305 feet tall If the angle of elevation of a ship to the tap of the statue is 241 how far to the nearest foot is the ship from the statue39s base feet Raised te the nearest feet Page 14 Student W 7 7 739 Ins h tor 113 math Aurelia pm Na xanwgs sig meni Practice Exam Date 7 Jackson Tracy Elliott Time Course Puma Math 113 TTR 048505 r 7 Book Blitzex Algebra amp Trigonometxy Se 33 Find the exact value of the expression if passible Do not use a calculator cos cos w 39 575 6 7139 6 q 71 u 6 3 7 7quot 39 6 323 Use a sketch to nd the exact valua of the expression ms 51 5 W an m 2 39 n 3 5 z 3 5 39 5 h 1 5 Page 13 113 math Aurore Ponta Nathan Assignment Practice Exam isms f Date 7 7 77 Jackson Tracy Elliott Time 7 Course Ponta Math 113 39ITR 048505 r Book B tzer Algebraamp Trigonometry Se 7 W 7 r N r 29 Find the exact value of the expression m 711 2 l 1 cos 39 Type yes answ iadians Type an exact using quotIE needed Else ietegers er actions for any numbers the expression 33 Find the exact value of the expression tan 1 quot 39 J 3 3 3 32 Find the exact value of the following expression possible Do not use a calculator 1 57r V I I I i 311 Sin quot i quot 6 I 7 7 Select the correct choice below and if necessary ll in the answer box to complete your choice CA 1 57 5111 111 We 6 Type an exact ense rerg as needed Type an integer er a simpli ed eetion 33 The expression is unde ned Page 12 5 Strident Date if math Ponta Natheh Aosignment Practice Exam Jackson Tracy Elliott Time Course P011123 Math 113 TTR i 048505 3 23 Book Blitzer Aigebra amp Trigonometry Se Use the following graph to obtain the graph of the What is the equation of the reciprocal lnction Figg hM goa39xquot 1 we function found by replacing sin with its reciprocal metion Give the equation of the function for the y M quot gtr graph that You obtam Type ahe ee39siioh as the variable Use 31 integers or fractions for any embers in re ii expression V sin 3 Choose the correct graph below 4 Graph two periods of the given secant function y 3 sec 3x Choose the correct graph below W m quot 39quotlt Page 11 t aen f Date Jackson Tracy Elliott 1 Time 7 7 Course Ponta Math 113 TTR O4amp05 223 ES 26 Book Blitzer Algebra amp T gonomooyo re Use a vertical shift to graph the function 4 1 z 2 X l E not L y Egg 55 3 EB 12 2 if L x iii Graph two periods of the giveiiafiin ent fu ction y H 2 tan ix Choose the correct graph of two periods of y m 2 tan below Graph two periods of the given cotangent mction l t3 y 5 on X 1 Choose the correct graph of two periods of y cot 31 below A j a c 4 a i quot A 2 s i 4 j 4 i 15 El j i bm s1 h39fT go has A Wiiiltll iiii M LLWLLJ Page 391 0 mamas 13 amga 1m mo Agoogo Praotico FiiiaiExam 39 image E Date illistrlictori 113 math Autoea P onta Nathan Assign lelit Practice Jackson Traey Elliott Time Course Ponta Math 113 TTR 048505 2 23 Detemu39ne the amplitude and period of the following equot Book Blitzer Algebra amp T gonometry 5e tits 5 inetion Then graph the mction we 1 9 The amplitude is QR 7 2 The period is D t 39 r Type an exact answer rising it as integers or eetions for any embers in the expreseionm 5 a i E qg 7 5e E Use the graphing tool to graph the function r eiieem 5 emerge 39 39 j or any an bexes Shawn with the gmpher 139 I 3 39 expression an emet answer Type the ward pi to insert the M w h A 73 symbol a as needed Determine the amplitude period and phase shift of fe the function Then graph the mction y cos x it 4 The amplitude is l t 3 39 39 39 quot e Lee 1 at The period is 7 7 777 3 39 Type an exact using 7 a needed Use integers or fractions for any numbers in the 57 The phase shift is E i 7 Type an exact answera g asneeded Use f 39 39i 1 I E integers or eetions for any numbers in the i Qi ri39 expressioeg t 39 Use the graphing tool to graph the function seeker 7 Emma 1 emeh K boxes shown with the grapher type an exam answer the word pi te the symbel 2 as nee ed Page 9 magi 39 Date Jacksan Tracy Elliott Course Ponta Math 113 HR 048505 39 Time 2 521 Book Blitzex Algebra Trigonom tly 56 r J 7 Determine the amplitude period and phase shift of the mction Then graph the function y sin 42 27 4 The amplitude isEl 7 i The period is 9 2 a Type an amt answ using naei f se 125 39 miegers m agtians for any Rumbas in the axpressionj 4giam V T The phase shift is lj Gym an exact answer 153mg is g I 5139 quot quot 39 integars gr ac39tians far all numbeis in the 7 39 quotI f 3 39 exprexion Use the graphing tool to graph the function Gimme Brim g9 gram 39323 Shawn with tbs grapher type an arms answer Typa the W611i pi in insert the symhei 1 as waded Determine the phase shift of the function 4 2 I 5 3111 x F39 y 2 HA 21m units down 75 93 1 units to the right 395 TE 5 units to the le 4n unitsup Page 8 sampucfor A cr Pd tmNa l nm ssignment Exam 7 V I asmden t I u 7 I Instruci fl 113 math Aux fa As ign i n ra tice H H 5 Date Jackson Tracy Elliott Time 7 Course Ponta Math 113 TTR 048505 Bunk Blitzcr Algebra amp Trigonometry 5e 1g Detem ne the amplitude period and phase shift if 4 at any of the given function Graph the mction f 1amp5 51 E w 39 1 g y 5 sm 2 gins 3 z 1 J y 51 251 g gt 6212 f The amplitude is 82 67 23 Simplify yam answer Type an exact answera aging as matted 7 4 The period is n 3975 Sp fy your answar Type an 3 as named The phase shift is 310m answer Type an exact answari usng 2 as needed Use the graphing tool to graph the flmction i can in 9 aniarge u 3 g Fm any answer boxes Shawn with the grapheer type an exam Type the worci pi t0 the symbol 5 as naedad Page 7 settle 39 397 f Date 39 inletaerial 3 math Accelerator newt rimLee Fine 3 quot 39 397 397 39 Jackson Tracy Elliott Course Ponta Math 113 TTR 048505 Time 3 l3 Book Blitzer Algebra 8r I gonome y 5e Use periodic properties of the trigonometric functions to nd the exact value of the expression tanm39 g 1 QB 1 ftSC 3 GD V3 Select the correct choice below and ll in any 7 711 Use the unit c1rc1e to nd the value of tan 4 and answer boxes in your Choicei h periodic properties of trigonometric mctions to nd I x 27 quotit 7 the value of tan f an exact answer using redlcglieiee needed Simplify your answer Rationalize in the deeominator iiquot 7 PW itquot i 2 i 2 I 4 B The solution 13 unde ned QT c 4quot4 zjoj quot X Select the correct choice below and llinftny answer boxes in your choice 772 quot Type an exact answer using redicale as oeetlecl your Rationalize the eerietor 533 The solution is unde ned Let sin t a cost t b and tan t c Write the expression in terms of a b and c 8 sin d t w sint 8 Sin t Sill t Simpli f your answer to t1 an 5 39 if 1 Page 6 39Siu39deiit Date Iiistructor 1i3 math Aurora Ponta Nathan Aesignment Final Jackson Tracy Elliott Course Ponta Math 113 1111 04amp05 39 Time 23 M iii Book Blitzer Algebra amp Trigonometry 5e Use reference angles to nd the exact value of the expression Do not use a calculator sin 765 I as E 2 E5 1 2 if 2 2 The point Pxy on the unit circle that eorresponds to a real number t is given Find the values of the indicated trigonometric function at t Find see L 4 4 39 3 15 13 we Let sin t a cos it b and tan t 3 Write the expression in tenths of a b and 6 sin t 10a v cos tl 2n tan t 911 sin t 1075 j cos If 21 tan tee 97 Simpii r your lquot i as xquot 39 39339 Test i 2 3 3 33 7 7 7quot Page 5 men 7 39 Date gt ensignment N Jacksom Tracy Elliott Course Ponta Math 113 HR 048565 Time it El 12 Book Blitzer Algebra amp Trigonometry 5e Find values of the nigonomet e functions of the angle in standard pnsition Whose terminal side passes through the given point Simplify answer ineluding ragieal integeg frs er aetiene fer any numbers the expreeeien cot 6 h E Simplify yew answer including sec 9 Snnplify year ans er inelnding Use integers er aetinne fer any numbers in the exnressienj cchxL J quot n Simplify you answer ineln img Use integers or aetiene fer anr numbers in the expreeeien A point 011 the terminal side of angle 6 is given Find the exact value of the indicated trigonometric mction of 3 w 2048 Find sin e 13 13 Find the reference angle for the angle 65 5 The reference angle is U D Page 4 Student 3 Date imam N133 5511 A ior puma Nadia Ass g t mega Final Em Jackson Tracy Elliott Time Course Ponta Math 1 13 TTR 048105 fa Book Blitzer Algebra amp Trigonometry Se 7 Use identities to find the exact value of each of the four remaining trigonometric mctions of the acute angle 8 1 sin8 5 Simplify yoi ESWiBI zadieaiigx Use integers or eetioms for any numbers the expxeesiom 739 amp Simpli i yourimwer algaljediggig Lise inte ers or fractions for any nominee39s the expression sec Di i Simplify yout eoswer iecluditige y integers or eetioes for any numbers in the expressiom I L I Shoplify your answer inch my radicals Use integers or aetions for my numbers in the expression Use a calculator to nd the approxilnate value of the expression Round to two decimal places sin 64 m fie 098 QB 100 390 092 To nd the distance across a lake 3 solveyer took the measurements in the gure shown Use these measurements to detemine how far it is across the lake Round the ewe to the nearest whoie number Page 3 Course Ponta Math asgr maquot391391mg maggisg ta 135 Essig m eatf iagiiee Fmi Egam Jackson Tracy Elliott 113 TTR 048505 BmlgfiB tzen Alggbra amp Trigunom tty 5t 7 r r I Use the Pythagorean Theorem to nd the length of the B missing side of the right triangle Then nd the value 39 of each of the six trigonometric mctions of B The length of the n ssingsidg 116 right triangle is a 3 Y ur answ r i113 expressigm cns t I YGIH MSWEI inchi jnquot g fa jg 3 expressia ta Simplify yemi m ar radicais amassing csc x yam answer radical expression sec 9 Simp fy yen mar any radicals cote E S np fy your war any mdicaals expressian U55 integefs r actians f0 any numbers 13921 the c26v Tl Usc integars m fragam fer numbers in the Use integers r actims far any nmnbers in the Use intng 31 atti s far 3113 numbers in tha Use a actians far any numbem in 113 Use iategers 0r a timzs far any the Find a co mction with the same value as the given expression cos 27 sin 63 78 sec 27 c39f 1 C 86 63 79 sin 27 Page 2 1 Student Date 39 imam lawman an Nathan regiment mam anquot Jackson Tracy Elliott 1 Time 7 Course Ponta Math 113 TTR a 04amp05 Book Blitzer Algebra amp Trigonometry 5e Find the radian measure of the central angle of a circle of radius r 1 meter that intercepts an arc of length 5 1400 centimeters 39 v The radian measure of the central angle is Type an integer er a simpli ed freshen Convert the angle in radians to degrees e121 radians V 39 12 radians Convert the angle in degrees to radians Bound to two decnnalhplaces Find the length of the are s on a circle of radius r intercepted by a central angle 9 Express arc length in terms of 1 Then round your answer to two decimal places Radius r 17 feet Central angle 9 325 s Lj feet L Simplify year answer Type yon answer in ms of 1 expression I39 39 3 39 se integers or fraetlens fer any numbers the 393 w s feet 39 Type yarn answer mended to two decimal places Page 1

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