MATH 1112 FINAL EXAM REVIEW - Valdosta State University€¦ · MATH 1112 . FINAL EXAM REVIEW . I....

MATH 1112 FINAL EXAM REVIEW

I. State the equation of the unit circle. a. 2 2 1x y− = b. 1x y+ = c. 2 2 1x y+ = d. 2 2 1y x− = e. None of these.

II. If 12tan5

x = − , find sin x for x in Quadrant IV.

a. 5 b. 513

− c. 513

d. 1213

− e. None of these.

III. Give the exact value of each expression.

1. 3sin2π −

a. 1− b. 0 c. Undefined d. 1 e. None of these. 2. cosπ a. 1− b. 0 c. Undefined d. 1 e. None of these. 3. sin150°

a. 32

b. 32

− c. 12

d. 12


4. cos 660°

a. 32

b. 32

− c. 12

d. 12


5. 3cos4π −

a. 22

− b. 22

c. 32

−

d. 1− e. None of these. 6. cos 0 a. 1 b. 0 c. 1− d. Undefined e. None of these. 7. tan 315°

a. 22

b. 1− c. 1

d. 22


8. cotπ a. 1− b. 1 c. 0 d. Undefined e. None of these.

9. 5sec6π −

a. 2− b. 2 c. 2 33

d. 2 33


10. csc0 a. Undefined b. 0 c. 1 d. 2 e. None of these. IV. Which of the following is a sketch of the graph of the given function on [0, 2 )π ? 1. siny x= a. b.

c. d. e. None of these. 2. cosy x= a. b. c. d. e. None of these. 3. tany x= a. b. d. c.

e. None of these. 4. coty x= a. b. c. d. e. None of these. 5. secy x= a. b.

c. d. e. None of these. 6. cscy x= a. b. c. d.

e. None of these. V. Simplify each expression. 1. cos( )θ− a. cosθ− b. cosθ c. sinθ d. sinθ− e. None of these. 2. sin( )θ− a. cosθ− b. cosθ c. sinθ d. sinθ− e. None of these. 3. tan( )θ− a. tanθ− b. tanθ c. cotθ d. cotθ− e. None of these. 4. sec( )θ− a. secθ− b. secθ c. cscθ− d. cscθ e. None of these. VI. Evaluate each expression.

1. 2arccos2

−

a. 74π b.

4π c.

4π

−

d. 34π e. None of these.

2. 1 3sin2

− −

a. 23π b. 4

3π c.

3π

−


3. 1 3csc cot4

− −

a. 53

− b. 54

− c. 53

d. 54

e. None of these.

4. ( )1tan 1− −

a. 74π b.

4π

− c. 2π

−

d. 6π


VII. Which of the following is a sketch of one cycle of the graph of each function? 1. 3sin 2y x= a. b. c. d. e. None of these. 2. ( )2cos 3y x π= − + +

a. b. c. d. e. None of these.

3. tan3

y x π = −

a. b. c. d.

e. None of these. 4. ( )cot 2y x π= + a. b. c. d. e. None of these. 5. 2sec3y x= a. b.

c. d. e. None of these. 6. 4csc(2 ) 1y x π= − − a. b. c. d.

e. None of these. VIII. Use the sum or difference identities to evaluate each expression. 1. cos 75°

a. 2 64− b. 2 6

4+ c. 6 2

4+

d. 6 24− e. None of these.

2. sin 285°

a. 2 64− b. 2 6

4− − c. 6 2

4+

d. 6 24− e. None of these

3. tan195° a. 3 2− + b. 3 2− c. 1 d. 3 3− − e. None of these.

IX. Let α be in Quadrant I, β in Quadrant III, 7cos25

α = , and 5tan12

β = .

1. ( )cos ?α β− =

a. 36325

b. 204325

− c. 323325

−

d. 204325

e. None of these.

2. ( )sin ?α β+ =

a. 253325

− b. 253325

c. 323325

−

d. 204325

e. None of these.

3. ( )tan ?α β+ =

a. 29119

− b. 253204

c. 317

d. 32336


X. Change each sum or difference to a product. 1. sin 68 sin 32° + ° a. 2cos50 cos18° ° b. 2sin 50 sin18° ° c. 2cos50 sin18° ° d. 2sin 50 cos18° ° e. None of these. 2. sin 5 sin 3x x− a. cos 4 sinx x b. sin 2x c. 2cos8 sin 2x x d. 2cos 4 sinx x e. None of these. 3. cos12 cos5x x+

a. cos17x b. 17 72sin cos2 2

x x

c. 17 72sin sin2 2

x x− d. 17 72cos cos

2 2x x

4. cos 20 cos 40° − ° a. sin10° b. 3 sin10° c. cos 20− ° d. 3 cos10° e. None of these.

XI. Let θ be in Quadrant II with 13sec5

θ = − .

1. sin 2 ?θ =

a. 2413

b. 120169

− c. 60169

−

d. 1013

− e. None of these

2. cos 2 ?θ =

a. 1 b. 1013

− c. 119169

d. 119169


3. tan 2 ?θ =

a. 120119

b. 245

− c. 120119

−

d. 125


XII. Evaluate each of the following expressions using the half-angle identities. 1. sin112.5°

a. 1 22+ b. 2 2

2+ c. 1 2

2−

d. 2 22−

2. cos157.5°

a. 1 22+ b. 2 2

2+ c. 2 2

2+

−

d. 2 22−


3. tan 67.5° a. 2 1− − b. 2 2+ c. 2 1+ d. 2 1− e. None of these. XIII. If the terminal side of θ passes through the point (-3,2), find sin 2θ .

a. 4 b. 1213

− c. 2 1313

d. 3 1313


XIV. Solve each equation for 0 2x π≤ < . 1. cos 2 1 sinx x= −

a. 50, , ,6 6π π π b. 20, , ,

3 3π π π c. 7 110, , ,

6 6π π π

d. 5,6 6π π e. None of these.

2. 1sin cos2

x x =

a. 4π b. ,

3 2π π c. 5, ,

4 4 2π π π

d. 5,4 4π π e. None of these.

3. 22cos sin 1 0x x+ − =

a. 5, ,6 2 6π π π b. 2, ,

3 2 3π π π c. 7 11, ,

2 6 6π π π

d. 5 3, ,6 6 2π π π e. None of these.

4. 23cot 2 1 0x − =

a. 2 5 7 4 5 11, , , , , , ,6 3 3 6 6 3 3 6π π π π π π π π b. 2 7 5, , ,

6 3 6 3π π π π

c. 5 4 11, , ,3 6 3 6π π π π

d. 5 7 11 13 17 19 23, , , , , , ,6 6 6 6 6 6 6 6π π π π π π π π e. None of these.

XV. Solve ABC∆ for the missing part. 1. 90 , 29, 21, ?A a b B= ° = = = a. 43.6° b. 46.4° c. 35.9° d. 54.1° e. None of these. 2. 5, 8, 10, ?a b c C= = = = a. 29.7° b. 97.9° c. 52.4° d. 7.9° e. None of these.

3. 40 , 6, 20 , ?A b B c= ° = = ° = a. 15.2 b. 8.1 c. 11.3 d. 5.6 e. None of these. XVI. Give the radian measure of an angle that subtends an arc of length 24′′ in a circle of radius8′′ .

a. 192 b. 3 c. 13

d. 3π d. None of these.

XVII. Convert 512π to degrees.

a. 75° b. 432° c. 15° d. 3° e. None of these. XVIII. Convert 260° to radians.

a. 913π b. 13

9π c. 46800

π

d. 139

e. None of these.

XIX. Simplify each expression. 1. sin secθ θ a. cotθ b. 1 c. 2sin θ d. tanθ e. None of these. 2. 2 2 2cos tan cosθ θ θ+ a. 1 b. 2cot θ c. 2 22cos tanθ θ d. 2sin θ e. None of these

3. csc secsin cos

θ θθ θ++

a. 1 b. sin cosθ θ+ c. 2 2csc secθ θ+ d. csc secθ θ e. None of these.

4. ( )2sin cosx x+ a. sin 2x b. 1 c. 1 sin 2x+ d. sin cosx x e. None of these.

5. 4 4

2 2sec tansec tan

x xx x−+

a. 2tan x− b. 1− c. 4 4sec tanx x− d. 1 e. None of these.

6. 21 sin

cotθ

θ−

a. 3cos sinθ θ b. cot secθ θ− c. cos sinθ θ d. cotθ e. None of these. XX. Change the product to a sum. 1. 6sin15 sin 45° °

a. 3 3 32 2

− + b. 3 32 2

− + c. 3 3 32 2

− −

d. 3 3 32 2


2. 4sin 3 cos 2x x a. 2cos5 2cosx x+ b. 2sin 5 2sinx x+ c. 2cos5 2cosx x− d. 4cos5 cosx x+ e. None of these. 3. cos 28 sin 40° °

a. sin 68 sin12° − ° b. 1 1sin 68 sin122 2

° − °

c. 1 1sin 68 sin122 2

° + ° d. cos 68 cos12° + °

e. None of these. 4. cos 7 cos5x x

a. 1 1cos12 cos 22 2

x x+ b. 1 1cos12 cos 22 2

x x−

c. 1 1sin12 sin 22 2

x x+ d. 1 1sin12 sin 22 2

x x−

e. None of these.

XXI. Let the point 2 21,5 5

−

be a point on the terminal side of an angle θ in standard

position. Find the sine and cosine of θ.

a. 2 21cos ;sin5 5

θ θ= − = b. 2 21sin ;cos5 5

θ θ= − =

c. 5 5 21cos ;sin2 21

θ θ= − = d. cos 5;sin 21θ θ= − =

e. None of these. XXII. For each of the following, give the quadrant in which the terminal ray of θ lies. 1. tan 0θ < and cos 0θ > a. I b. II c. III d. IV e. None of these. 2. csc 0 and cot <0θ θ> a. I b. II c. III d. IV e. None of these. XXIII. Give the reference angle for the indicated angle. 1. 211° a. 149° b. 59° c. 31°

d. 391° e. None of these.

2. 59π

a. 18π b.

9π c. 19

18π


3. 2.3

a. 2.3π − b. 2.3π + c. 2.32π−

d. 2.32π+ e. None of these.

XXIV.Find the quadrant in which the indicated angle lies.

1. 34312π

a. I b. II c. III d. IV e. None of these. 2. 278− ° a. I b. II c. III d. IV e. None of these. 3. 5.43 a. I b. II c. III d. IV e. None of these.

4. 2135π

−

a. I b. II c. III d. IV e. None of these.

XXV. Which of the following angles are coterminal with the given angle? 1. 43− ° a. 137° b. 677° c. 47° d. 227° e. None of these.

2. 1312π

a. 3712π b.

12π c. 25

12π

d. 1312π


XXVI.Give the amplitude of the function ( ) 7cos5 13

f x x π = − + +

.

a. 1 b. 7 c. 5 d. -7 e. None of these.

XXVII.Give the period of the function ( ) 8sin 9 32

f x x π = − +

.

a. 8 b. 2π c.

9π


XXVIII.Give the period of the function ( ) 2 tan 3 64

f x x π = − + +

.

a. π b. 3π c.

4π


XXIX.Given the following data set for ABC∆ , how many triangles can be drawn?

1. 12, 20, 25a b A= = = ° a. 1 b. 2 c. 3 d. 0 e. None of these. 2. 8, 15, 33a b A= = = ° a. 1 b. 2 c. 3 d. 0 e. None of these.

XXX. If 5cos7

θ = − , θ in Quadrant III, find the value of tanθ .

a. 2 67

b. 2 65

c. 52 6

d. 72 6

e. None of these.

XXXI. The length of an arc of the unit circle is as given. Name the quadrant within which the terminal point would lie.

1. 35

t π=

a. I b. II c. III d. IV. e. None of these.

2. 1312

t π= −


3. 2059

t π=


4. 3.78t = a. I b. II c. III d. IV. e. None of these. XXXII.Give the terminal point on the unit circle for an arc of the length below.

1. 76

t π=

a. 3 1,2 2

−

b. 3 1,2 2

− −

c. 1 3,2 2

−

d. 1 3,2 2

− −

d. None of these.

2. 34

t π=

a. 2 2,2 2

−

b. 2 2,

2 2 − −

c. 2 2,2 2

−

d. ( )0, 1− d. None of these.

3. 53

t π=

a. 3 1,2 2

−

b. 3 1,2 2

−

c. 1 3,

2 2

−

d. 1 3,2 2

− −

e. None of these.

XXXIV.Complete the following statements: 1. 21 sin _____θ− = a. 2tan θ b. sinθ c. cosθ−

d. 2cos θ e. None of these. 2. 2 2sec tan _____θ θ− = a. sec tanθ θ− b. sinθ c. 1 d. 2cos θ e. None of these. 3. 2 2cos 7 sin 7 _______x x− = a. 1 b. sin14x c. cos14x d. 0 e. None of these.

4. 1 cos50 _____2

− °=

a. cos 25° b. sin 25° c. sin100° d. cos100° e. None of these. 5. 21 cot 9 ______x+ = a. 2csc 9x b. 2cot 10x c. 2sec 9x d. 2cos 9x e. None of these. 6. ( )cos _____θ π+ = a. cosθ b. sinθ c. sinθ− d. cosθ− e. None of these. 7. ( )sin 2 ____θ π+ = a. cosθ b. sinθ c. sinθ− d. cosθ− e. None of these.

ANSWERS: I. c II. d III. 1. d 2. a 3. c 4. c 5. a 6. a 7. b 8. d 9. d 10. a IV. 1. b 2. a 3. a 4. b 5. b 6. a V. 1. b 2. d 3. a 4. b VI. 1. d 2. c 3. d 4. b VII. 1. d 2. c 3. c 4. a 5. a 6. a VIII. 1. d 2. c 3. a IX. 1. b 2. c 3. d X. 1. d 2. d 3. d 4. a XI. 1. b. 2. d 3. a XII. 1. b 2. c 3. c XIII. b XIV. 1. a 2. d 3. c 4. a XV. 1. b 2. b 3. a XVI. b XVII. a XVIII. b XIX. 1. d 2. a 3. d 4. c 5. d 6. c XX. 1. a 2. b XXI. a XXII. d XXIII. 1. c 2. d 3. a XXIV.1. b 2. a 3. d 4. b XXV. 1. b 2. a XXVI. b XXVII. d XXVIII. b XXIX. 1. b 2. d

MATH 1112 FINAL EXAM REVIEW - Valdosta State University€¦ · MATH 1112 . FINAL EXAM REVIEW . I....

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