10` \0

PreCalculus
Chapter 4 Exam
Trigonometric Functions
______________
Name___~~
~~_~
r: -r
T-+---­
Period~
l',--",=",,-E
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
\3B
1) 138°48'17"
-t
(1-8')-t(__
ll_) =
bD
A) 138.81
B) 138.76
Convert the angle to degrees, minutes, and seconds.
2) 340.96°
•
139 . 80
3l:.0 L'
q10 (~O)
=
~
51, b
I(J
--=C_
2)
A
0) 138.86
C) 138.80
,L
1)
(I (\) == 3b
VJV
A) 340°57'36"
Convert from degrees to radians .. Use the value of 7t found on a calculator and round answers to four decimal places, as
i44
needed.
3) 144°
0
11 :::
IBO
~4n
4TT
.
5
~3n
5
1\
3)
C)~
5
~~
5
5
Convert the radian measure to degree measure. Use the value of n found on a calculator and round answers to two
10' ­
~
decimal places.
4)
~~
1 it 180 J =­ 1
'2'
i SO
\0
l>
4)
\0
B
-­-=::......-_
C) 257.14n°
A) 154.29°
Use the arc length formula and the given information to find the indicated quantity.
5) s = 18 em, e = 54°; find r
30
A)-- cm
5)
120
B) - c m
s=r 8
Solve the problem.
60
C)-- em
1t
7'(
t {\\\lSt
D)
71
be
\f\
r(l(hu~
1
"3 cm
\~~ r.... ,.317
54 "*" _.J1.·ill
\
"TT
180 -
r::: Jl ~ = ~o/Tr
\0
6) The radius of a car wheel is 15 inches. How many revolutions per minute is the wheel making ' -;iI
when the car is travelling at 30 mph . Round your answer to the nearest revolution.
A) 3318 rpm
~ -tInct
CJ\fLiJ mierence
G= Zn r
G:71T
B) 9 rpm
C) 336 rpm
rev
?01
+
I tr.
6)
C
D) 2101 rpm
12-1-fr . 5280.J1
~
-+ft'
C
If(\!
->t
~o ~
\ft(
\ 1(\
ot\"
l{) ffi \1'\
(15)
G~ 30 IT"
:..
1
\ ~ \2 -¥ 51 BO ..y 60.:t I
30'IT
41' \
.I(
\
-*'
I -\-
~O
-- 33~
rpm
SHORT ANSWER. Write the word or phrase that best completes each statemen t or answers the q uestion.
Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms.
7)
Jor
B~~___1_5____~
7)
X·
e
~ P~tt lOj(Hecth Thm
17 Q Z-t b '1 = C 2
15 2.. t- X 1..." III A
Xl ~ 1'12 . lSI Find the values of all six trigonometric functi ons. Cf rO~1 BJ l
SOri CAI1 lOA
Slrl
SIll
e'"
COS
e"
functions.
csc6 =\lIB cot e= Is 18
tQr\6 = 8f (5
i
and that 8 is an acute angle, find the values of the remaining five trig
)2. 1 5 L
l OA
8)
=C 2.
sm e=
\
/fib
Give the exact value.
1'(
be\ouJ
--m
sec e '" -f2I /s
cot e'" 5
9)
faA
3
see
(See=
caSe = 5/fih
tone ~ I/S
5
9) tan
-ISI. ='{3
sec9",ll[15
15/11 8) Given that tan 8 =
X::1n
see belo\,}.)
I
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use a calculator to find the fun(CtiOn valcue t,o fo~,r )de:lim ~ Pl2acel s'1 \
e
A~<\\~
'-, ~~
10) esc 21°6'19"
&111 2\ · 10 \q
A) 2.5908
B) 2.0719
"'-
.
C) 2.7771
10)
C
11)
D
12)
A
D) 1.0719
Use a calculator to evaluate the function. Round your answer to 4 decimal places.
11) cos 0.2261
A) 0.2300
B) 1.026
C) 0.2242
D) 0.9745
Give the exact value.
12) cos 150
A)
0
-J3
2
B)
-J2
C) _
2
-J3
2
2
D) _
-J2
2
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
l1T 13
Find the measures of two angles, one positive and one negative, that are cotenninal with the given angle.
13) ~
11
2
3-+
3
1\=
iT _
-llT
d
3
2lT = - SIT
13) _
51T f ~
~
___
J
3
Suppose that 8 is in standard position and the given point is on the terminal side of 8. Give the exact value of th"
indicated trig function for
e.
'
..,
)
l
(-8
J' t (2 ... -=- C
64 "14 c Z
"7
14)(-8,2); findtan8andsec8. ( _ e~.l)
14)
sec e ~-~B
:0
c=:·
2
Evaluate without using a calculator.
~, if sin ~ =- :0 and tan 8:> 0
15) cot
+j+A_
T
Solve the problem.
tOf\
5!n < 0
4La·. () e,.,- --'2,"a. __ -1/-'4
IB
[J
b8
G?PIQ(u
=-
~ ~~
'-I - 1
teArl >0 ~
C
I • ~
(-
1) 1+ bl..:. 10 1
16) A 32-foot ladder is leaning against the side of a building, If the ladder makes an angle of
_
16)
'f... -=-
I=) 3
ft.
24 36' with the side of the building, how far is the bottom of the ladder from the base of
the building? Round 0 r answer to the hundredths place.
0
Sln ( 2 ~ 0
31
3G' ) =- ~
31
~9(\QQ
x
Wi
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the value of the unique real number 8 between 0 and 271 that satisfies the given conditions.
iOIl >0 '=" Ii j
.sin <. G ~ .:l! I-l
17) tan 8 = 1 and sin 8 < 0
.
'
{l.
#C
A) 7rr
C) 371
B) 5n
4
4
I
(I
I
D) 71t
4
215
,
':;rr
--
B
17) _ __
"-fz 6
T C
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Graph each of the following trigonometric functions over a two-period interval (problems 19-22).
Period '. Zrr
18) Y '" -2sec x
\-r
1
19) Y=
~V ·
sin 3x. Identify the period and amplitude.
OS 3x ~ ZiT Pe-nOd .
~
3
:U:
YI
18)
see
Qe\
19)
see
be\G~~
IjJ
20) _
20) y '= tan x + 3
_
_ __
P3
31TJ
I
•
I
1
I
~
2J) Y 5 co, [3 x + ;]- Iden;Uy 'he ,mpli'"de, period: ' .nd
F\mp
=
Find the exact value of the real numbery.
22) Y '= sin-
1
[fJ
0 ~ 3x - In
5
Per \ocf:
21) _ _
+,L
_ __
phase shd-t· left 1rh
2IT
3
-fur an 9\e~ !)
--5 IS Clcrc.JS
(lOG K\flj
IZ/1-{3
t PoSItIVe ~ or
P~'''hift.
v
Jr(;(f1
&0" ClnSIe
23) y == arctan (1)
23)
1 ~oSltlVe ~ OI
Solve the problem.
1
24) A ship travels 87 km on a bearing of 22°, and then travels on a bearing of 112 0 for 136 km.
24) ---L..>O
llo<..I!. ._
K;.....:.._
1Y\
Find the distanc from the starting point to the end of the trip, to the nearest kilometer.
I
I
p
(~l ~)
I
-t
(13~l)
1~Ob5
X.
7.
:: X2
I
~ X
\~\ ~tn
I
25) A contractor needs to know the hbght of a building to estimate the cost of a job. From a
point 88 feet awa from the base of the buildin I the angle of elevation to the top of the
building is found to be 44° 27'. Find the height of the building. Round your answer to the
hundredths place.
-­
tOr\
(4~C If) =~
88
00 . tOf)(~4°11'r
X~ 8!0 . 33 5t.
25)
S~ . 33
St.