_______________________________ NaDle _
MAT 1093 Test 1 Review
S olve o n s eparate p aper a nd s elect t he b est r esponse.
MUL TIPLE CHOICE. Choose t he o ne a lternative t hat b est c ompletes t he s tatement o r a nswers t he q uestion.
D etermine w hether t he r elation r epresents a function. I f it i s a f unction, s tate t he d omain a nd r ange.
1) {(-2, 7), ( -1,4), (0,3), (1,4), (3, 12)}
C ) n ot a function
B) function
A) function
d omain: {-2, - 1, 0, 1,3}
domain: {7, 4, 3, 12}
range: {7, 4, 3, 12}
range: {-2, - 1, 0, 1,3}
D etermine w hether t he e quation i s a f unction.
2) x2 - 4y2 =1
A ) function
B) n ot a function
D etermine w hether t he e quation d efines y a s a f unction o f x.
3) = 5 x + 3
Y x +2
A) function
B) n ot a function
F ind t he v alue f or t he f unction.
.
4) Fmd f(x + h ) w hen f(x)
A) 3x + 3 h + 7
S x- 5
S olve t he p roblem.
5) I f f(x)
:
3 x+ 7
=-S--.
x-5
B) 3x + 3 h + 7
C ) 3 x+ 7 h
Sx + Sh - 5
8 x- 5h
D ) 3x + l Oh
8 x+3h
= f(2) = 0, and f(-7) is undefined, what are the values of A and B?
!,
A ) A = - 7, B = 2
B) A
C) A
2/ B = -7
7, B = -2
D ) A = - 2, B
7
T he g raph o f a f unction f i s g iven. Use t he g raph to a nswer t he q uestion.
6) W hat is t he d omain o f f?
20 Y
- 20
A) all real n umbers
C ) {xix ~ OJ
B) {x 1-20 :5 x :5 20}
1
D ) {xl-16:5x:522}
Find the domain o f the function.
7) f (x)
x
= .I
",x-9
B ) { xix> 9}
8) h (x) =
C ) { xlx;ll!9}
D ) { xlxl!:9}
B) (xlx;ll! O}
A ) a ll r eal n umbers
C ) a ll r eal n umbers
D ) {x Ix ;II! - 8, 0, 8}
x- 4
x 3 64x
A ) { xix ;ll!4}
The graph o f a function f i s given. Use the graph to answer the question.
9) F or w hat n umbers x i s f(x) > O?
20 T
- 20
B) [-20, -12), (14, 20)
A ) (-12, =)
C ) ( -12,14)
The graph o f a o ne-to-one function is given. Draw the graph o f the inverse function -1.
1 0)
5 Y
(1,4)
-I
(-4, 2)
-I
1
2
3
4
5x
2
-3
4
5
2
D ) ( -= - 12)
B)
A)
5 Y
5Y
4
4
3
3
( 4,2)
2
-5
-4
-3 -2
(4, I )
-5
1
-4
-3
5x
-2
-I
( -1,-4)
(-2, -4)
-5
D)
C)
5Y
4
3
-5
3
- 4 3 -2
3
-4
4
5x
(4, -2)
r
I
(1, - 4)
-5
-5
The function f i s one-to-one. Find its inverse.
11) f (x)
8 x2 - 9, x ~ 0
A) -l(x)
1
C) - (x)
Ix
x +9
.~
=-v8 8
12) f(x) = -5x + 1
-9x- ~
8x + 1
- 9x + 5
B) -l(x)
= - 5x + 1
13) Which angle f3 is a positive coterminal angle of e
A)
f3:::: 7 n
C) -l(x) = - 5x + -5
- 9x- 8
- 9x - 8
B)
f3::::
D ) -l(x)
= - 9x + 5
8x + 1
6; .
4671
7
D)
P== 48 IT
7
3
D raw t he angle 6.
1 4) e
= _ 3'71"
4
A)
B)
C)
D)
C onvert t he a ngle to a decimal form i n d egrees. R ound t he a nswer t o t wo d ecimal places.
15) 17215'53"
A ) 172.32
B) 1 72.2r
C) 172.27
D ) 172.26
C onvert the angle to DO M' Sft form. R ound t he a nswer t o t he nearest second.
16) 51.33
A ) 5119'33"
B) 5119'36"
C ) 5119'54"
I f s d enotes t he l ength o f t he arc o f a circle o f r adius r s ubtended b y a c entral a ngle 8 , find t he m issing q uantity.
17) r 11.0 inches, e = 3 0, s = ?
A) 5.5 in.
B) 5.8 in.
C) 3 30 i n.
D) 280 in.
18) r
1
= 2" feet, S:::: 8 feet, e
?
C ) 16 r adians
A) 4
D ) 4 r adians
19) Salt L ake C ity, U tah, is d ue n orth o f F lagstaff, A rizona. F ind t he d istance b etween S alt L ake C ity (4045'
n orth l atitude) a nd F lagstaff (3516' n orth l atitude). A ssume t hat t he r adius o f t he E arth i s 3 960 miles. R ound
t o n earest w hole m ile.
A) 397 m iles
B) 3 79 m iles
C) 407 m iles
D ) 27,713 m iles
4
C onvert t he a ngle i n d egrees t o r adians. E xpress t he a nswer i n e xact form a s a m ultiple o f 71..
20) -480 0
C) _ 8 "
D) _ 9"
B) _ 7 "
A) _ 3 "
4
3
2
8
C onvert t he a ngle i n r adians t o d egrees.
21) 1 h
12
C ) 1500
B) 160 0
A ) 1650
D) 2100
I f A d enotes t he a rea o f t he s ector o f a circle o f r adius r f ormed b y t he c entral a ngle 0 , f ind t he m issing q uantity. I f
n ecessary, r ound t he a nswer t o t wo d ecimal p laces a s n eeded.
22) r = 35.1 centimeters, e =
;
r adians, A ::?
C ) 4 30cm 2
D ) 2 15cm2
C) 31.416 ft2
B) 6 8.4cm 2
A ) 6.1 c m2
D ) 15.708 ft2
F ind t he a rea A. R ound t he a nswer t o t hree d ecimal p laces.
23)
6 ft
A ) 2.618 ft2
B) 5 ft2
S olve t he p roblem.
24) T he b lade o f a windshield w iper s weeps o ut a n a ngle o f 1350 i n o ne cycle. T he b ase o f t he blade is 12 inches
from the pivot point a nd t he t ip is 32 inches from the pivot point. W hat a rea d oes t he w iper c over i n o ne
cycle? (Round t o t he nearest 0.1 s quare inch.)
A) 948.3 i n2
B) 1105.3 i n2
C ) 1036.7 i n2
D) 1041.8 in2
25) A n o bjed is t raveling a round a circle w ith a r adius of 10 meters. I f in 15 s econds a central angle o f 3 r adians
is s wept o ut, w hat i s t he linear s peed o f t he object?
1
2
B) 3 m /sec
D) 2 m/sec
A) 3 m/sec
C) 3 m / sec
26) In a c omputer simulation, a satellite orbits a round E arth a t a d istance from t he E arth's surface of 2.7 x 104
miles. T he o rbit is circular, a nd o ne r evolution a round E arth takes 10.1 days. Assuming t he r adius of t he
E arth is 3960 miles, find the linear s peed of the satellite. Express t he a nswer i n miles p er h our t o t he n earest
whole mile.
B) 17,189 m ph
C) 128 m ph
D) 803 m ph
A) 700 m ph
5
I n t he p roblem, t i s a r eal n umber a nd P = (x, y ) i s t he p oint o n t he u nit c ircle t hat c orresponds t o t . F ind t he e xact
v alue o f t he i ndicated t rigonometric f unction o f t .
27)
( $1,2.)
6
F ind sec t.
6
A)
$1
28) ( :' -
f)
A) _
q 6$1
B) 6
5
5
D) 5 $1
11
11
q $5
D) $ 5
Find csc t.
9$5
B )-
65
$5
9
9
4
U se a c alculator t o f ind t he a pproximate v alue o f t he e xpression r ounded t o t wo d ecimal laces.
29) p cot 0.1935
A ) 5.10
B) 0.20
q 0.98
D ) 1.02
30) csc 64
A) 1.16
q 1.11
B) 1.09
D ) 1.04
Solve t he p roblem.
31) I f friction i s i gnored, t he t ime t ( in seconds) r equired f or a block t o s lide d own a n i nclined p lane is g iven b y
t he f ormula
2a
t=
g s ine c ose
=
w here a i s t he l ength ( in feet) o f t he b ase a nd g 32 feet p er s econd p er s econd i s t he a cceleration o f g ravity.
H ow l ong d oes i t t ake a b lock t o s lide d own a n i nclined p lane w ith b ase a = 9 w hen e = 29? I f n ecessary,
r ound t he a nswer t o t he n earest t enth o f a s econd.
A ) 1.2 sec
B) 1.1 s ec
q 1.4 sec
D ) 0.3 sec
A p oint o n t he t erminal s ide o f a n a ngle 6 i s g iven. F ind t he e xact v alue o f t he i ndicated t rigonometric f unction o f 6.
11
32) ( - 3' 5 )
F ind c os e .
A ) _ 34
3
33) ( -2, - 1)
A) -5
q 1!
D ) 3 $4
34
q
B) _ 5 $4
34
D)
5
F ind csc e .
B)
-J5
-2
--J5
S olve t he p roblem.
34) T he p ath o f a projectile fired a t a n i nclination e t o t he h orizontal w ith a n i nitial s peed Vo is a p arabola. T he
r ange R o f t he projectile, t he h orizontal d istance t hat t he projectile travels, is f ound b y t he f ormula
v o 2 s in2e
R
w here g = 32.2 feet p er s econd p er s econd o r g == 9.8 m eters p er s econd p er s econd. F ind t he
g
r ange o f a projectile fired w ith a n i nitial velocity o f 124 feet p er s econd a t a n a ngle o f 34 t o t he h orizontal.
R ound y our a nswer t o t wo d ecimal places.
B) 442.64 ft
q 534.05 f t
D) 442.74 ft
A) 267.02 f t
6
35) For w hat n umbers 8 is f(8) = sec 8 n ot defined?
A) integral multiples of 1 (180)
B) all real n umbers
q o dd multiples o f ~ (90)
D) o dd multiples of 1 (180)
36) W hat is the range of the cosecant function?
A) all real n umbers from - 1 t o 1, inclusive
B) all real n umbers
q all real n umbers greater t han o r e qual to 1 o r less t han or equal t o-l
D) all real numbers, except integral multiples of 1(180)
Use t he p roperties o f t he t rigonometric functions to f ind t he e xact v alue o f t he e xpression.
37) sin2 f3 + cos2 f3
A) 1
q
B) 0
2
D) -1
For t he g iven i nformation, find t he e xad v alue o f t he i ndicated t rigonometric f undion o f e.
~l,
38) Given that tan 8 = -
8 i n q uadrant II.
39) Given t hat cos 8 =
~,
B )-
40) Given t hat sin 8 =
~,
..[j5
+,
" ,35
42) Is the function f(8)
A) e ven
$3
4
4
..[j5
$3
7
B) cos 8
= - ,.J35, tan 8 = - ..[j5
D) cos 8
3s
tan 8 = - ,.J35
S olve t he p roblem.
41) I f f(8) =esc 8 a nd f(a)
1.
6
7
sec 8 < O. Find cos 8 a nd t an e.
A) c os8= - 6-' t an 8 =
cos 8 = -
D) _
149
F ind s in e.
t an 8 <0.
A)-./33
D ) _ -../149
7
q --
149
10
A)
q 7-../149
B) 7-../149
A):1Ei
q
Find cos e.
.J35
= 6, t an 8 = - 3s
6
35
=6, find the exact value of f(-a).
1
q6
B )-6
sin 8 + cos 8 even, o dd, o r neither?
B) n either
7
D )-6
q o dd
Use transformations to f ind t he e quation f or t he f unction o f t he g raph.
43)
y
x
A)y=3sin
~X
D) Y
8 ) Y = 3 s in2x
1
- 3 S Ullx
W ithout g raphing t he f unction, d etermine i ts a mplitude o r p eriod a s r equested.
44) y = sin 5x
Find t he p eriod.
A ) 27r
5
1
45) Y = - 2 c os 3"x
A)2
46) f(x) =
!
D) 1
C) 67t
D ) 27t
C) 37r
2
D) 3.
F ind t he a mplitude.
8) -2
cos ( - 4;"1: x) Find t he period.
A ) 87r
5
C) 5
8 ) 27t
8 ).!
2
3
A nswer t he q uestion.
47) Use t he g raph a nd/or t ransformations o f b asic trigonometric functions t o f ind t he e quation o f t he g raph?
3
16n
8) Y
-3
sin(4x)
C) y = 3 co(4x)
8
48) Use the g raph a nd/or t ransformations of basic trigonometric functions to find the equation of the graph?
2
4
- 1t
Ol~--~--~----~--- 3
C) y
= -2 sin(3x)
G raph t he s inusoidal f unction u sing k ey p oints.
9
2
1
4
49) Y = - cos ( - -x)
6
Y
4
2
-21t
21t
41t
61t
81t x
-2
-4
-6
A)
B)
6
Y
6
Y
6
-6
9
D ) Y = - 2 cm(3x)
D)
C)
y
12
10
-10
-12
-6
F ind a n e quation for the graph.
50)
y
x
-4
-5
A) y
= -5 sin (2x)
B) Y = - 5 cos (2x)
D)
F ind t he phase shift.
51)
1 ~J
Y=- 3S
X
-
A) ~ u nits t o t he right
C) - 3 u nits d own
52) Y
B) - 3 u nits u p
D) ~ u nits to the left
- 5 cos(8x + n )
A) 8 n u nits to the right
B) ; u nits to the left
C) ~ u nits t o t he left
D) 5 n u nits to t he r ight
10
Y=-5COS[~X)
S olve the problem.
53) A t own's a verage m onthly t emperature d ata is r epresented i n t he t able below:
M onth,x
J anuary, 1
F ebmary,2
M arch,3
A pril,4
M ay,5
June, 6
July, 7
A ugust,8
S eptember, 9
October, 10
N ovember, 11
December, 12
A verage Monthly
Temperature, o f
31.4
33.1
45.3
57.3
74.0
83.1
85.7
81.1
81.1
5 95
44.7
36.2
Find a sinusoidal function o f t he f orm y
A) y 85.72 sm(O.49x - 1.92) + 31.48
C ) Y 27.15 s m(052x - 2.09) + 5 955
=A sin ( wx -
cj + B that fits t he d ata.
B) y = 28.41 sin ( 052x - 2.11) + 59.10
D) Y 31.47 sm(0.52x - 0.79) + 85.73
54) For w hat n umbers x, - 2rc :s x :s 2rc, d oes t he g raph o f y ::: sec x h ave vertical asymptotes.?
B) _ 3';"[ _ .2 ';"[ 3';"[
2' 2 '2' 2
A) - 2, - I, 0, I , 2
D ) n one
G nph::;;nrc:i:~;j at
least one
period.
6Y
4
2
-21\
-2
-4
-6
11
B)
A)
y
6
Y
4
2
x
-2
4
-4
6
6
D)
C)
6
Y
4
2
x
x
2
4
-4
6
-6
12
A nswer Key
T estname: 1093 TEST 1 REVIEW S12
1) B
2) B
3) A
4) B
S) A
6) B
7) B
8) 0
9) B
10) A
1 1)0
12) A
13) 0
14)
I S)
16)
17)
A
0
0
B
18) C
19) B
20) C
21) A
22) 0
23) 0
24) C
2S) 0
26) 0
27) C
28) A
29) A
30) C
31) A
32) B
33) 0
34) 0
3S) C
36) C
37) A
38) C
3 9) 0
40) B
41) B
42) B
43) A
44) A
4S) A
46) B
47) 0
48) C
49) A
SO) B
13
A nswer Key
Testname: 1093 TEST 1 REVIEW S12
51)
52)
53)
54)
55)
A
B
B
B
C
14