\' Namel
Ans'er K<l
College Prep
Midterm Review
\,
P acket
Midterm Dates:
ln Class
&
s
1.
ln the accompanying diagram of a unit circle, BA
tangent to circle O at A , CD it perpendicular to
the x-axis, and OC isa radius.
is
I.
2. Circle O
ad toe.
has its
centeratthe origin, OB =1, and
'l ('
\l/
t
Which distance represents sin9?
@co
(dl BA
(a\ oD
(c) oB
3. lf tanA<0 and cosl>0,inwhichquadrantdoes
lA
lf ruZBOA = d, which line segment shown
length equal to cos d ?
terminate?
Y
(a)
(c)
angles is coterminal with
100"
4. lf tan? < 0 and cscd > 0,
I
terminate?
6. ln which quadrant
does the angle
It
does
the angle 274 lie?
8. ln which quadrant
does the angle
to radian measure and express the
answer in terms of n .
i) l\
lLd)''., 1r160o
T
lre^,
4fr
l5
aoE
r5
t,'
radians
-
-165o lie?
E
lf
11. Convert
112' lie?
@
7. ln which quadrant
9. Convert
in which quadrant does
x
(q) -260"
zoo'
180'
a
CA
1g.
5. Which of the following
-820'?
has
to degrees.
tr-
10. Convert 210' to radian measure and express the
answer in terms of n .
alc.
L2. Convert
fl
lc'
I l\
U)
7ln
radians to degrees.
l8
ir(i*",)
l8
=
=
llD"
fr.
ncosd
=-1
13
.na sind >0, what isthe value of
1
L4.
lt tan0 =-fa
and angle
d
lies in the second
J
quadrant, what is the value of cos 0 ?
tan??
la
lano= .S
:1$
coso=
fr= -
t+ *= cL
13=cl
15. lf
I
is an angle in standard position in quadrant
lll and sind = -!,
all remaining
t7' "ralrate
,rV. I
trigonometric functions of d.
-8 [
csc,E
co:o
-
tanx>0.
C.bLO
t-l-
l5
LosO
-!
=
l-1
=
}ano
CC,t
is an angle in standard position, evaluate all
remaining trigonometric functions of
and
=
SecO
16. lf x
O
sero
-ll5
=
-a
-Ea
3
[a
=
cole
;-)
-9-
2
--L- -a€
=
hnD
!-5
8
x if sinx = -+
I
'-=
.6
{L
3
=€
l5
17. Evaluate: sina+
18. Evaluate: 2cos60otan30o
r(|)(. q)
63"orL
SneD. r CO)@"
=
tr3
*'5=l
19. Evaluate: cos30osin45osin30o
@
J5-.6."
-!-=
Aaa\i
20. Express sin320o
as a sin function of a positive
acute angle.
- Sin 4D-
411.. Express
cos215o as a cos function of a positive
acute angle.
acute
-
-_SirrqS:
^-ir
u
27
24. Find the exact value of cos300o.
-rla
CoS
e
SecUD' =
It,
-Stca0"=
:
29. Express cosl2To
as a
-*
-a\.-3
- seLs
.
3
30. Express tan265o
SrvlU-lo
as a function of a positive acute
*an 8'5"
as a function of a positive acute
cos(S,e
- csc 3q"
:
co\ 5"
32. Find the measure of angle A if 0" < A <90"
-1f)"
=
sinlo.
Sn-latYl
Le6
='lD
= loe
ft=ll
g"
cot 210"
angle less than 45".
angle less than 45o.
a
-a
?. = .6
Cot 3C'=
function of a positive acute
-CoSSd = -
I
of secl2O".
28. Find the exact value of
.
angle less than 45o.
3L. Express sec231o
= !a
kO"
Find the exact value
= E
. Find the exact value of sec 510o
S€c\SD" =
J3
CSC
25. Find the exact value of tan330o.
tnn3D"
as a csc function of a positive
angle.
co535'
23. Find the exact value of sin225o
'
22. Express csc157o
and
-7
;3.
Find the measure of angle
cot (2A + 21)"
A if
0" < A <90o and
= tan(B A* 9) " .
clc
aA ra.\ tl3i1 t ci =
l5R t 3Ll) -clD
34. What
is
the range of
35. What is the range of
thefunction y=3sinx?
the function
y = 4cos3x?
..l (-
.)-
-q!\LLl
j
15tl:tuO
A ={
36. What
the
amplitude of the graph of
the equation
y = 4sin2x?
is
4
40. What
y=
is
37. What
the
amplitude of the graph of
the equation
is
'v = 2sin[1r),
\2)
38. What
1-
5sln-x /
=
7
=
42. What
is
!:2sin3x?
u3
!
=3cos4x?
4
4=fl
7
43. Write the equation of the graph below.
2 v
1
x
2x
-1
-2
\_
I
ir
\-
the
41. What is the period of the graph of the equation
Y = -6sin2x?
LtTf
the period of the graph of the equation
is
frequency ofthe graph of
the equation
e
2
L\I
39. What
the
frequency ofthe graph of
the equation
Y = -sin2x?
,
the period of the graph of the equation
is
COS
LX
. Write the equation
of the graph below.
45. Write the equation of the graph below.
2
1
-1
a
-):i^ )-x
J=|sirazx
46. Write an equation for the sine curve whose
period is
2n
u(
and whose amplitude is 3.
47. Write an equation for the sine curve whose
period ls
4r
and whose amplitude is L.
21
<=
fl
P=t
$-n =
$_l
2t
T-z
rll = 35inx
48. Write an equation for the cosine curve whose
period ir
'3
4
and whose amplitude is 4.
49. Write an equation for the cosine curve whose
oeriod is
'22
A
and whose amotitude is
U-v
f-z
|=s
*l
'l = sin)'x
: Llcos3X
4rt=Fn
f =q
1.
Sketchthegraph of
I
y= ^sin2x overthedomain 0<x<2tt'
ih, !
.44. sketch
!.
the graph of y = cos 2x over the domain 0 < x < 2n
'
5\
i\
-Lw
u\:
ffinx
overthe domain
03x
<Ztr
.
,/ha
3
\
I
/
\
I
\
\
f
\
JT
/1
g
\
/
t
t?
t
\
f
r
/
t
\ /
$.
Stcetctr
t
the graph of y
I
- -cotix
over the domain 0 < x
<2r
\
fxr
,
a
\
/
f
\
t
z
f.
r
\
"r
'
nfI
r2
I
ET
2t \)
,5t
5$
What is the value of
2)
| t.
a,n Lrc"
la
cls(00"
2)
COS IBLJ
_l_
,ls
j-
a
s1. tn MBC, o=3,
b
=8 , and mlC = 60o . Find
the length of side c .
.z
d=G'
C'=
Ar"rt f ),
I
"or(
I
|
What is the value of
cos(lrctanf),
Lin( orr"orl),
/
5b
What is the value of
rY>
- ,f,c\b cosc
t'- 8' -rt3\ex.cottd))
e
a
5$. ln MQR,if p =7 ,
r to the nearest tenth.
Q
= 9, and mZR= 160o, find
f '= ?" 1' - eylcosR
Y'= 1" ,'q-- a(l)(qXco:lroc)
qq
['= ]Lft.ulotZ"t..
('=
l- = ls.-ltoo-15..
-
-
f N lS.x
\-
sq. ln MMN , I =7 , m =8, and n =
CC5L
5.
Find
= ty, *vt - ,l''
S-t'
a[t)ts)
nn4
I
L= t 0
88. ffre
sides of a triangle are 5, 10, and
largest angle to the nearest degree.
5q
xi
A"'q
14. Find the
)2rC--
7\,-
.lrrr n
CoSL= E'*
mll.
LosB:
tf
t S-l.-{L-
lL)
.
tt
r&J
rn+B= i35
6$. tn LABC , mZA = 42" , mZC = 58o
Find a to the nearest tenth.
ln MQR, mlP =63", mlR=8lo,and p=80.
Find r to the nearest tenth.
f= =-P
SnR - ,;i',rP
c 1 .. tic)
-C
tivr A StrrC
(itD
..............__--.._..--==
brr\92" )in5t"
-
= .lOir, Al?"
Si r15S-
Ct= l,XqUZ.^
T'urBt' >nb5'
f Si,rl r:i - Sr S'r \t l"
Srr \t' 5
S,"/, S
f = 88,r.otrorrt
f a tt'r
A2s-l.q
tn MBC , a =15 , c =20, and mZC = l00o .
the measure of acute 2 to the nearest degree.
O'S.
CLC
5
_r5 _
aO
sin
l1
SioA
h&
---:-
r\L
-=,r.
srr-\A
t:inB
rq
$rrr $
Sn rar'
-
-E)\(\tS:
=
,l3g{s
-
SinA
4t
5'
Za
{n 4fr=
tl}"
.ln MBC, o=6,b=70,and
the area of LABC
6tr. tn MBC, mZA=38", a =48, and b=19. Find
the measure of acute ZB to the nearest degree.
rn 4b =
mZC =30o. Find
.
K= |c.b:,rrC
K: l(t'Xrot(sirr 3D)
K= 15
l.-1"
6S. Find the area ol LPQR to the nearest integer if
p=7, r=8,and mlQ=63".
K= If"s,(\Q
K = l(r)(s[sirruS)
K= ),t.q.tt.
K*a5
.
To the nearest tenth of a square centimeter,
what
is
the area of the triangle below?
69.
what
is
the area of the triangle below?
P
6cm
L
K= L'Lrosin P
K-- L ocsrn$
K= !Qo)[ro{si,1 l2o')
K= !(to(r.o)[sirllsD
K= t5
(=
u13.30r. . .
Kt
q3 3
Ld(i How many different triangles can be constructed
given the parts mlA= 45" , a = 40 , and b =36?
&= =
-,b
Sint'l - Srt$
LIO 3rr
.+L)
Sirr$ = , u3ro'{
rQel + .
]r.t, How many different triangles can be constructed
given the parts mlA = 150" , a =10 , and b =12?
ab=
ffi-
>t11t5" :>lrlB
4QS,nB= jg,5ir1HS
\o
)
,-.lD'
f ' LtO'' - LtS = $,5' /
1I . i.{),, ..\S - ttS X
iD S,rll5d
snB
la
Srn$
-,D=,'.b= E5inllr}"
rO
iO
KeF+ sI
T" 5J' -15D"' lt']" X
_ _f,
g.
ir.f
5rt>u. = ?qd'X
r{f . now many different
triangles can be constructed
parts
given
the
m./.E
=105" , e = 18, and -f =l5t
I
,
l.-+
I sinE
srn tr
rt
15
Sff>" =
7fu How many different triangles can be constructed
given the parls mZA=23", o=15, and b:18?
c\
i5,_4
SnzS'
SrrtF
s
irlt)
lSSit'\b-= lB:sin?3
-_--=-
rS.Sr,lF= ?5sinr05
)x
I^
l)
is
rt
SnF = .8C,Hq
(ei +, 5'1"
Srnb = .{utcl
Re
[
+'
e'b
T'. a8'.lC '
T : l>L" ?3'
'T- ' 5t" r- IOS = l3cl" '/
'[r : lLU"r lD5'= 33i' X
+-
[t)
21. fwo forces have magnitudes of 25 and 40 pounds and act upon a body at an angle of 67" between them'
Find, to the nearest pound, the resultant of these two forces.
b,= Gtr Lt-
;1ctccosb
b'* qo', &*-
3"(uo[z:[rr'''-il5)
b'= 5.1,13rJ"'
b-=
55
lbs.
,
C..:oS
SiAL=
r0l
,3q18
rn 2;L =
,]5
Find, to the nearest degree, the measure of the angle between two forces of 30 pounds and 35 pounds if
the magnitude of the-resultant is 42 pounds.
L':>
A
- r_
}bek tcelr {o51s\=
iglJ" -'ioo =
co:)B --
,ED"
e't Lt- b'
'1 crC
cosB=@
4e';Xeo)
rn
7S
-
Aot
,1lcD
+b= ?Oo
Express as a single trigonometric function:
cos d(sec d
-
cos
d)
I - cosl>
>ir'\tD
7x.
Express as a single trigonometric functio
n,
tune=
sec
!rrlO
7ps3 = 'yr9',LliJi= SnD
-j-urk
CJ>92
I
0
{.
Express as a single trigonometric function:
.wz 0-cot2 o-sil2 0
cv-
I - Srl=O
t*r't>
80.
co,5'o
I
'
Express :---------;- as a single trigonometric
I
+cot'9
function.
*) _ =
5inzB
80. Wfrictr expression
sin 22o cos I 8o + cos 22" sin I 8'
(a) cos4Oo
(c) sin4"
i>io (aa"
(a) sin 80"
(c) sin 60'
@
(d)
cos 60o
cos 80o
8t.
CDS\JrO'
?
@ sin+0"
t 18 ") = 5i114C"
Prove the statement sin (90'
* 0) = cos d .
)irl(A t b) = brnA cosB r cosfi sirlib
r tcsqO' Sing
S\ n(9d r t) = \,.1D" tc:O
==
Co: t7C' -lC) =
to
(b) cos4'
CSC"()
8O. The expression cosT0ocosl0o+sin70osinl0o is
equivalent to
is equivalent
:)::rt
"(r)bi'rt))
/lt,
8*.
Prove the
statem.nt
"@
co':, (A - B) =co:r\coi5$
Co)G -
r$)
g5. nna tr,e
r ._\r uf sinB)
=co:e)Co:\8$'. )rr6Si rtrtD"
=
"
cos(4s"-30.).
r
(o:e)1-r) t (:,n u\u)
LD: (n -b)
cc:(+S
=
tc:tl co\R + .:rr-r A:inb
*'f rEl';'.*;
., a' ., :ltt
a
: - CDSL]
: Gq.+*6
=
b.,
80. Find the exact value of cos 1056 by using
cos (45'+ 60.) .
8lI. tf sin I
co5(At$ = ClSrl Cr)Sb - sinl+ si rrb
cos.B =
Co{qf. Od)-
value of cos(,< + a).
Colx 5"CCL hLl' - 5,rrQ{Si nL00
q, !A a -E-,-E
a-a
= 6_@
qq
=
= J5-iu
L-
"J-
-15
=
f13
J__k_+ ri 7-
tt
with angle I in quadrant il and
with angle .B in quadrant llt, find the
co5((1 t E=
rDlf,cc:B- srirAsinb
=f
'.X+) (i"Y.?)
1
89. A and B are positive acute angles. lf
sinl = 1
,
and cos B
find the value of sin(l - B).
=:.
13'
Sn(A-B)
cosAsrnB
= SnAceb-B-
8q. The expression 1-2sin2 45o has the same value
as
@ cos 90"
=(txt)
("J(e
| /1,
Iq=3b2o
tos
W
(b) sin22.5o
(d) sin 90o
(a) cos 45o
cosz(+:)
'.g5
= J\,
(p5
I
I
QB. rne expression cos' 40o
value as
L
-
sin2 40o has
the same
(b) cos20'
(a) sin 80'
(c) sin 20'
@)
tt.
lf sinl
=1)
CobZft
cos80'
cbsz(\c)
and angle
I
is acute,
find cos2l.
= t -aSn'A
> \-a(.?Y
= l- .?(*)
= 25 - -l-u-
=72s
Z>
9D lf cosd=-1 ,nO 6
is in quadrant ll,
find cos20.
5
the value of sinZA.
c's-rD=jl$,-,
'a(ft)= \tS
a'
'
r
eS
75 e>
=-L25
5\rrZA
=
}5irIA
CCSA
a(a)ts
'2- aq
a5
t,
gB. ft .B is a third quadrant angle and sin B =-3,
find sin 28
il.
.
gS tf A is apositive acute
the value of sin1,,l.
,,m
v I
90. lf
,4 is a
the value of
='( P.)[:;
cosin=,f_#=
cosl = 1, find
.
lf
IIf
ii
lol\'
.
i5u,"
of
l?
Co\X= ZD
\f+
S$. find, to the nearest degree, the solution set of
8cosx +2 = 0 over the domain 0o ( x < 360o.
ur"
\'a
a
V
Find, to the nearest degree, the solution set
20 cot x -13 = 0 over the domain 0o ( x < 360o .
9f
Janx = ?9
i5
Rel 2\' 51"
L 5lm' !51'
:I
ReC4 ' I
=
t, -1
;'l- T
=Vfyq =3
EE,E 6.5
-lib-E',(5.=
cosx= -+
!A
, find
I
positive acute angle and
:-Vs-E
l.j
$,fi
=,fr
.or1l.
---<
rs
2
3ir1Z$= AsrrrBcos6
angle and cos A =Z
fi.
to the nearest degree, the solution set of
16sin2 x =9 overthe domain 0o ( x <360o.
Find,
SiflrX = fr
gir\X = t 1
r?eI
+ 4'1"
a"q1'
][r
l3\"
N-
3\\"'
/l
. Find, to the nearest degree, the solution set of
tarr2 x +3tanx= l8 overthe domain 0o ( x < 360o.
lcrrl'x r 3\nvrx - \b = C-l
(trn K { L-e\({qvrx - a)= o
lqnx- - u
R<la, t\"
-E: qq"
1S: l]_lcl"
1r.rX
]'anx= 3
Re[ a .
r,
rrr
]a'
Ja"
J53"
= f;l U1*q(r)ti0, '4trTf
. Find, to the nearest degree, all values of x in the
interval 0o ( x < 360" that satisfy the equation
-K
6cos2.r+cos.r-1=0.
("*
(pcosx * dacosK - r\ '= o
CoSK =
Re [
\'
3 -t
*
5G-x--4
*. co:( :
_-
Lo0'
I
Ret a'.
t"
tr'. IZO' '=: Jl'
m"'Eqo E:2Sq'
-t t- T4_;,(dto
i'r r-.x =
{.")
kirtX = a
"|6rr\X= - L.o
L():K=
CCf>'*
10O. Find, to the nearest degree, all values of x in the interval 0o ( x < 360' that satisfy the equation
3sin2x+8cosx=7.
S
(r- co:;x)
t Bcc-,sK =
3^ 3ccsax +8co:x=
-J
Sc\uhu,r
Re$
:L'
-19
L
(3x - r-o)(ax -z)
I
- 3Cc,1. \ + Bco:K _ u\ =O
3costn - ScoSx t u\ =O
(cosK - a)(acos K - a-) '= o
Co\A=a LO\'r(=Z
)$;
iL
/\
4' 4t"
L{X"
3
fcrS K =
-'$ t fi:.-\(-tx*i)
zQ
c(-.:'( - '-B r
i
i)
l\c
_LC
fii : 3\)"
ftr)
a
=
Z.
2
J
Cc-'5r(-* 3
© Copyright 2024 ExpyDoc
