Math 1160 Exam 3
T, n
Name
Student Number
Lab Section
ftoone-
q 3qs ?6
fG
All questions are worth 5 points each. There is no partial credit on the multiple-choice
questions.
SECTION
LAB DAY
& TIME
CODE TO ENTER
FOR SECTION
(2 diqit code)
1A
T,8:00-9:15
01
1C
T,3:00-4:15
02
LAB
.f,
'h.
G
,7
a
It.
t'e
.13
1D
T,
:00-12:15
03
.1E
R, 11:00-12:15
o4
1F
T, 9:30-10:45
05
1G
R,8:00-9:15
06
1H
R, 9:30-10:45
07
1J
R, 8:00-9:15
08
11
Question
Points
MC
Total
ClC
I\4ATH I 16O: PRECALCULUS
EXAM III, VS. A
Wednesday, October 27, 2OO4
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
rr T{d'
5-ts f6
Find the trigonometric function value of angle 0.
1) tan e =
-A
and 0 in quadrant
II
al
1"43 "'
i.--tQ;?5
Find cos 0.
^, 3lE
atT
_.
Dt-
i.1#
,
O
f:
*"1'{:
3 iIt
6 rrr
^f
,4
-**:
dl3
'i-e.*
s
al'3
- lE
D)-M
'25
E) None of these
Multiply and simplify.
2) cos 0 sin 0 (sec 0 A)cos2e-1
B)sin0-cos0
csc 0)
{
l{c tp i * /t *.:*
C {'{
:*Pt JI
Cos o s,^ o
# '{- "
c)1
D)sin0-2csc0
-3in *, rSa,*1
-.\ +
1 i'a"9
$,
E) None of these
-*
i
(. v.j
n'
Find the measures of two angles, one positive and one negative, that are cotenrrinal with the given angle.
3) -45"
.#,
* Llf
A) 135"; -1.35" o TL t
'-q9
8)3L5";-225"
'
C)135';-225" # " )- --i"*<*
4;
'r
\ -D) 315"; -405"
E) None of these
Evaluate exactly.
4)
cosff. tni",'
A)
-
E=Z-t,
1)
^E(^6
nl_1EM_rl
^\ ^litnls - D
-t-T
-
JJo
uS;, i-- ,e--'
9.t*rb
*)F
t
?f*
;
&2
--F*'
{ *;L#f * 3o)
S:^t{5 {,."3*
F
.. I
{_u"l c{5 iol la
r/"f;
/ \i-
/4't
!
I, .?)
"+"\. |\ *f.? Ii
'f:
,l
E) None of these
M1160 EXAM
*
i
t-
6
\I*-:
.i
\,i
III vs.A, page
1.
of 8
r'
n?. \r'\\
\t\
i.
)i?
./\*1
ti'
.\t"-
i
i:"
'-*/@
ri
*9
,1.
,,,.
J;
*
*n
re.
#1lffi:H::ffi::5t*ttt{t#'J;"#t*;1:'*;
s)Abrirnp,:l::::;:::$:iil'ff
one
west and
il: ;;'"s'! rne'!er?
i $.r-. V"" "9
rjrl*r"::i:
o, tzoo^/-a
'ul
+ 1200 m
nooJ'*
12oo
C)z+Oo^/am
m
^
'
"'I
A)
^. --revolutionsperminrrte
f;o'Br
per minute
revolutions
*
-.4 n
\-/
revolutions
Assusre
,i
,"'"
n/
.
-
I
W ;
[.{.9
,
{r_A
,j
",,.,''
i of
* s
"=}
) .i , -1,
':b "{ '\
?-
ii
,:.8
4oo
r."r;'
l'"1;
;;
i-l
f--
*-
. .,- r-nctiofl.
frrnction'
;onocretric
ffi
"\'"
i:gr
l
ri
l-a
off,
'
ll,,J t'
*+_
",W
.{-
of these
E) None
M1160 EXAM
111
vs'A'
Page
2
ol
I
d
t
\*--//
minute
;1;:6;'ff.;;:
;W
urffi
\
..,"'
o"l
t
minute
Per
4 revorutions per
^,
D)?'o'
.;.
' t- -'
nr-ri
.i
---
K
Determine the domain and range of the function.
8) Y=sin2x+3
A) Domain: (--, -); range: [- 3,31
B) Domain: (--, -)i range: [3,4]
C) Domain: [3,4]; range: (--, -)
D) Domain: (-*, -); range: (-4,4)
E) None of these
Find the exact values of the indicated trigonometric functions. Write fractions in lowest tenns.
S's
l{ -'
--."€
de
Find sin B and tan
A)sin
ba
7
-2's'-
ii:
*-
*
B.
u=*,tunB=h.
g=4
7'
7
C) sin B = L; :rrnB =-h
B)sinB=P;tan
D)sin
U=#,tunB=T
E) None of these
Solve, finding all solutions in [0,2n).
10)
sin(x.,)
-*,[. i) =)
^\L.U
.' ^t bb
u)i'+
^,7n 1Ln
L)z-'T
i€,\Xi.t-c.rr
r {,n 1r r ss,I,/\- (tor,r Cbs
\. -
sijy(-r5 *e
*.b in x
")+
E) None of these
i),a ,x
-
Suox
f,..g :, -t
M1160 EXAM III vs.A, page 3 of 8
€-f t
\
:;" +
g i",
x f;s Si,
dt
sJ
,
I
11)
2sinxcosx+cosx=0
!,5n,fu,1
A) x =
'
,S'''"a" i-
d c;.r5
2'6'2
X '; a
.J
6\
n 7x 3n
Dt A=-,
"t^- 2, 6' 2,
LLn
6
C) No solution
5n 3n 1l.n
vl^ n
2'6'z'
5
vt
A=
E) None of these
+
Convert to radian measure. Leave your answer in terms of
12) -510'
36b
A)
-+
b
u)-#
,,;w&,.
3te
- :;S'- - {a
-lto"n,p {s
t4o
r
l?s ;*5# =
-#d.'+
t0
l8
* lt
lv
f"
?
,.?
(r
I
,)_*
")-{T
E) None of these
Find the exact function value.
1.3) sin 390"
3p#
A);
1
B)
^6
ar&
v,/
2
k
,.tI
I.
o)*
E) None of these
Find the exact value.
14) Given that cos 0 = - 5/13 with 0 in quadrant II, find tan 20.
A'-'
{t{
L69
120
'Xr":
S-t+$t* t?'
e-f 4$
720
_. 120
**
"i-uA
td?
r?
€
JTq'{
119
fr
\
F
h\
7L9
D)-'
-'
-rA'{r"
t?
1.69
ut-' 119
Z4*'^
--7
t * tt"'6
E) None of these
M1160 EXAM
III vs.A, page
4 of 8
"1u\
at
etn
.-g-:
tl.r
-a{
e
A{gr}
;m
ht-{4) t-4
€,t
#v,
t4
.H
*
g:
13t
i
Find the exact value by using a half-angle identity.
15) sin 22.5"
5n^
A)-1
'2
t
{ - CaS6
,)-+"t;E
t2
.)+
7G
at-'
e*?
-
*
z {;^
e
t
,d--
4dd"6d
*
BJ=;
A)y=cos(2x)
B)y=*,[ar,J
c) y =,-[+-]
D)y=-2sinx
*=L
6
L<
€i
lntB
E) None of these
M1160 EXAM
III vs.A, page
5 of 8
]t
e
Find the trigonomekic function value for the angle shown.
17) sin 0
cf
n
t&
* 3o"
t< ;
-9.od
5'^ =
q
-
5
A) sin e =3
5
B) sin
O
=94
C)sin0=-9
4
D)sin0=-9
5
E) None of these
t.
Answer the question.
18) Find cos 0 given that cos 20 =
land
92
0s0<
:''/
*J
iu
,J*
g.
riL
+$
A)6
CAF}
B)g
'25
5o'll
^l%
6
"r+
,1"*&t
E) None of these
q
=
1'
{( +{'t tt
CosQ.
7
t9
[os*a - S,n?*'A
/,Es t/1t'G)
L?J
tf
fM1160 EXAM III vs.A, page 5 of 8
fil-re : (r
(a=J
tQ
6r.
*r
\
"?
{r
-t€
t{
Evaluate.
1e)
.or-r :l3)
,ir, [z
s)
L
al-
)L
/-)
(o5
\:\J
5,n
A
{t l4 5
€
Jb
73
B)+
z5
_. 14
c)'25
D)+
E)None o f these
Simplify the expression.
- ^. cos4 x - sin4 x
Lwl
n
cos4x-srn2x
A)
(tus'x
---*"**"*z-.^*
(Ps
X
- J,n<jr
! cos"x*
1
B)_+
$r^?A
*'e"***-'%.q*;*-*..ff
Lp#'
cos2x-sin2x
c)_1
"'
,or2 x - sin2 x
E) None of these
Find the sign of the six trigonometric function values for the given angle.
2r) -297
A) Positive: cosine and secanti negative: sine, tangent, cotangent, secant
B) Positive: sine, cosine; negative: tangent, cotangent, secant, cosecant
C) Positive: all
D) Positive: tangent and cotangeni; negative: sine, cosine, secant, cosecant
E) None of these
I
?Lt
.a
,'J
Tt*'*r+ai-1
*--{l
Write in terms of the cofunction.
22) sn41"
A) cos 49e
I
$*'^ { }i'
B) cot 49"
C) cos 41'
.i6i
D) tan 49"
-$-*
E) None of these
M1150 EXAM
III vs.A, Page
7 of 8
$
5e,*
{sF4
_
Without using a calculator, give the exact trigonometric function values with rational denominators.
23) tan 60'
A)
^6
-/{r
D;
1
/^\
^, "E
r"tT
a
b.G
-/ +
L
d
.'''
u)z
-}
h
E) None of these
Simplify.
24) (sin x - cos
A)
x)2
* &o5 ,,.
(S''o
1- 2cos}x
B)L-cosx
C)1+cos2x
D)1-2sinxcosx
S
r^:A
i ( ,'^; - c" " )a
r ZSr^;..Ce-)x
+ eo5 A
/ g'.-xco5x
[ -
E) None of these
Find the amplitude, period or phase shift.
25) Find the phase shift of Y = -4-
N
n)
+to
f
c)f
*C
a
"*['.."-J
the right
to the left
F
lr.L
rts
t
4
to the right
3
nt -I- to the left
-'12
p)
H,84 to the left
M1160 EXAM III vs.A, page 8 of 8
*9
fr
1'7-
FILL IN THE BUBBLES FOR THE CORRECT ANSWERS
,
2
3
4
5
6
7
8
e
@@oo@
@o@@@
@@@o@
@@oc@
0@@@@
@@@e@
0@@@@
c@@@@
o@@@@
,o @@o@@
,1 0@oco
12 @ooo@
13 0@o@@
t4 @@o@e
15 @@oo@
,6 0foo@
t7 0@oo@
18 @@oc@
,e o@ooE
20 0@o@@
2t @@(E@@
o@@@@
23 o@@@@
22-
24 @@oc@
25 @@@o@