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# Precalc AlgebraTrigonometry MAC 1147

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This 12 page Class Notes was uploaded by Duane Bayer on Wednesday September 23, 2015. The Class Notes belongs to MAC 1147 at University of South Florida taught by Jogindar Ratti in Fall. Since its upload, it has received 295 views. For similar materials see /class/212636/mac-1147-university-of-south-florida in Calculus and Pre Calculus at University of South Florida.

## Reviews for Precalc AlgebraTrigonometry

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Date Created: 09/23/15

Review problems for Final Exam MAC 1147 MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question In the problem P x y is the point on the unit circle that corresponds to the real number t Find the exact value of the indicated trigonometric function of t 1 ZZVZ Find cost 9 9 A 7 7 B 2 9 C 94 77 Find the exact value Do not use a calculator 2 cos 3n cot 311 A 1 unde ned B 1 unde ned C O unde ned Find the exact value of the expression Do not use a calculator 3 co tE sin 3 3 3 Ay 2 EALgdi CW Use the given information to find the quadrant in which 6 lies 4 sin9gt0 and cos 9gt0 A Quadrant IV B Quadrant II C Quadrant III 493 D 0 Dquot 3 6 D Quadrant I Find the exact value of the indicated trigonometric function of 6 from the given information 5 tan 9 2 9 in quadrant II 5 Find cos 6 A a quot29 13 5 59 c a 5 429 5 29 29 Find the reference angle for the given angle 8n 6 4 A E B E C i 8 4 4 we 3139 D 4 1 Find the exact value of the expression 7 IE cos 4 7 Use the Pythagorean identities to find the exact value of the expression 8 Given cos t and sin tlt 0 find sin t 8 Asint i Bsint2 Csint 8 Dsint 34 5 5 5 5 Solve the problem 9 A new homeowner has a triangularshaped back yard Two of the three sides measure 65 ft and 9 80 ft and form an included angle of 125 The owner wants to approximate the area of the yard so that he can determine the amount of fertilizer and grass seed to be purchased Find the area of the yard rounded to the nearest square foot A 2129 sq ft B 5200 sq ft C 4260 sq ft D 2130 sq ft Find the amplitude period or phase shift of the given function as requested 10 Find the amplitude of y 4 cosX 121 10 A 4 B 4 C E D ii 2 2 Graph the function over a one period interval 11 y z 4 sinX 4 11 A N C N Nwagtuu I39 wwwxsu 6anth has B Write the function in the form y a sin bx c ory a cos bx c Find the period and phase shift 12 4 sin 39rcx 2 A 4 sinvx period 4 phase shift 2 I C 4 sinv period 2 phase shift 2 71 Find the exact value of y or state that y is unde ned 1 13 y cos 1 AIL 6 ii ii 771 B 4 B 4 sinnx 2 period TE phase shift 2 D 4 si11nx 2 period 2 phase shift 2 11 DEL C 6 12 13 14 y tan 1 14 A g E 733 C if D 15 y sin 4 15 A 4 B O C n D Unde ned 16 y CQS391 COS 16 A 35E B C quotE D Solve the problem 17 A sprinkler rotates back and forth through an angle 9 as shown in the gure At a distance of 4 17 feet from the sprinkler the rays that form the sides of angle 6 are feet apart Find 6 A 37 B 56 C 74 D 28 18 Ifsinx andE lt xltn find secx 18 I77 r 247 7 94 55 A 2 B 77 C 77 D 9 Use the fundamental identities and the given information to nd the exact values of the remaining trigonometric functions of x 19 tan X and sec X 19 4 4 Asi1r1gtlt c05x 34cscX cotx i 5 5 3 Bsinx icosx cscx cotx 5 5 3 mp m4gt Csinx lcosxicscx cotx 5 5 3 D sinx cosx cscx cotx 5 5 3 3 Use the fundamental identities and appropriate algebraic operations to simplify the expression 1 tan2 X sec x A 1 B sec x 20 C sec x 2 21 COS X cos x sec x sin2 x A sec2 x B act2 X C c562 x Find all solutions to the equation Express the solution in degrees 22 sin X J 2 A 135 860 n or 315 360 n C 225 360 n or 315 360 n D csc x D csc x B 45quot 360 n or 315 360 n D 240 360 n or 300 360 n Use the fundamental identities and appropriate algebraic operations to simplify the expression 23 C03 X tan x 1 sin x A 1 B secx C sin2 x Find all solutions of the equation in the interval 0 211 24 3tanXl 0 Na 19n mm 25rr 0L m 12 12 12 12 12 12 25 sin 4x i 2 A E n B o CL l2 l1lr il5 lli9 D 126312612312 44 26 seal l2 2 ANTn23 1237 0amp3 2 2 4 4 4 2 phi N131 D cos x sinx D 20 21 22 23 24 25 26 27 tans 43min a 1 0 AIl 31 r r 332 goLIE 3 3 282c052x 10 Use trigonometric identities to solve each equation in the interval 0 2n Z91cosx25in2x AAT114IL B Krill114 3 3 6 6 Find the exact value of the expression 30 cos 45 30 A ux2 B I542 4 2 31 tan 165 A 2 NE E 2 Find the exact value of the expression Without using a calculator 32 sin 21 cos 5 cos 7 sin 71 24 8 24 8 1 A 39 B 1 2 tanl tan 15 15 33 1 tan L tan E 15 15 A J B i 2 2 c 1331 D Jami 3 2 3 3 3 OdinE D EmE 2 4 0 12 115 Ian IE 0J2 i i 2 2 0 quot D393 27 28 29 30 31 32 33 Use the information given about the angle 6 to nd the exact value of the indicated trigonometric function 34 sin 6 6 in quadrant IV Find fan 29 34 A B l C D 7 7 24 7 24 Use an identity to write the expression as a single trigonometric function or as a single number 35 2 tan 30 35 1 tanz 30 A 1 2 B 212 C J D 2 4 3 36 1 2 sinZ 13 36 12 Ni B C 2 D3 2 2 2 2 Use half angle formulas to find the exact value of each expression 37 sin 225 37 mix2mg B 2 IE C 2 2 D1 2 5 Use the information given about the angle 6 to nd the exact value of the indicated trigonometric function 38 tan 9 3 11lt 6 lt Find tan 38 IE 1 IE 1 ll 5 1 Iii 1 A B C m D quot quot 39 3 3 3 3 Find all solutions of the equation in the interval 0 211 39 tan 2x tan x 0 39 A 0 B J E 211 271 El m 12 6 3 12 6 12 3 C 0 n 2n D 3 4 4 40 sin 2x cos x sinx 40 T4 4 4 4 C o m 39l D 071 mm7E 3 3 4 4 A f gin mi 31111 B 01211122 1m Find the value of the indicated trigonometric function of the angle 6 in the figure Rationalize the denominator where necessary 41 5 I 7 Find sin 9 74 Iii 547 4 192 A B C D 74 y 5 74 7 42 42gt 6 I 5 Find cote Iii 54E IE NE A 5 B 11 C 6 D 11 Use the given trigonometric function value of B to nd the requested trigonometric function value of the acute angle 6 Rationalize the denominators where necessary 43 tan 9 Find cos B 43 3 5 3 4 A B C D 5 3 4 5 Find the trigonometric function value of the corresponding complimentary angle 44 Given that cos 64 z 04384 find sin 26quot 44 A 08988 B 04877 C 04384 D 22812 Solve the right triangle angle C is the right angle Round to the nearest tenth where necessary 45 B 180 c 39 45 AA720 a29b 26 B A720 al2b37 C A720 a37b 29 D A720 a37b12 Solve the problem 46 From a distance of 45 feet from the base of a building the angle of elevation to the top of the 46 building is 64 Estimate the height of the building to the nearest foot A 40 ft B 22 ft C 92 ft D 20 ft Solve the triangle Round the answer to the nearest tenth 47 B AC97 a88 mb157m BC108 a9mb16m CC103 a444 mb251 m DC103 a16mb9m Solve triangle ABC Round the answer to the nearest tenth 48 B 376 C 1110quot b 376 inches A A 314 a 321 in c 575 in B A 294 a 575 in c 321 in C A 294quot a 5950 in c 3410 in Solve the SSA triangle Round answers to the nearest tenth when necessary 49 A 73 a 33 b 67 A B28 C79 c 75 BB28 C79 c81 CB79 C28 c79 D No triangle exists Solve the triangle Round the answer to the nearest tenth 50 B 30 A a z 73 B z 78quot C 2 378 B a z 73 B 7 78 C 1422 C a z 83 B m 69 C z 1431quot D a z 83 B z 28 Cu 1472 Solve triangle ABC Round the answer to the nearest tenth 51 a 168 b 185 c320 A A 237 B 132 C 14310 B A 237 B 263 C 130 C A 2 263 B 237 C 130 D No triangle exists D A 314 a 3410 in c 5950 in 47 48 49 50 51 Solve the problem 52 Two ships leave a harbor together traveling on courses that have an angle of120 between them 52 If they each travel 547 miles how far apart are they to the nearest mile A 547 mi B 41 mi C 947 mi D 1894 mi The vector v has initial point I and Terminal Point Q Write v as a position vector 53 P13 8 Q11 12 53 A 2 4 B 24 4 C 24 20 D 2 20 Determine whether the vectors AB and CD are equivalent 54 AG 8 B 3 1 C0 0 and D 4 7 54 A Not equivalent B Equivalent Find the expression 5 u 3 12 v 12 45 Find u v 55 A 9 27gt B 9 27gt C 15 3 D 15 3 Find a unit vector u in the direction of the given vector 56 4 3 56 4 3 5 5 3 4 A B c D 2015 5 5 4 3 5 5 lt 7 Find the expression 57u4i 6jv 7i3j Find 7u 8v 57 A 84i 66j B 15i 15139 c 28i18j D 3i Si 58 lfv5ij andw8ij39 Findllwwll 58 A 54 B 1173 C 3 D I97 Find u o v 59 u 5 42 v 6 11 59 A 162 B 127 C 102 D 126 Find u v where 9 is the angle between the vectors u and v Round the answer to the nearest tenth 60 M 7 ll vll 5 e 31 60 A 408 B 14 C 108 D 30 Find the angle between vectors v and w Round the answer to the nearest tenth of a degree 61v3i2j w4i 5j 61 A 1624quot B 85 C 723 D 451quot Let v and w be two vectors in the plane with given magnitudes The angle between v and w is 6 Find the expression Round the answer to the nearest tenth 62 quotle 11 Ilwll 13 e 58 Find Ilv ml 62 A 222 B 282 C 332 D 4661 Determine whether the given vectors v and w are orthogonal 63 vlt33gtwlt 6 12gt A Not orthogonal B Orthogonal Determine whether the vectors v and w are parallel 64v 4 3 w 201 A Parallel B Not parallel Plot the point having the given polar coordinates 65 4 225 63 64 65

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