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2)
Do the following for the angle,
0
= -7n/3, C{rCWrl;SL
a) Sketch the angle in standard" position.,,
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b)
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n
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Determine the quadrant in which
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3)
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b)
c)
Determine the quadrant in which the angle
lieq.
1
W;rr
/7
Drl
-/tt
7,t-<
Determine one positive and one negative coterminalangle forthe given angle, in both
degrees and radians.
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4)
Convert the following angle measure from degrees to radians. 450o
//fo,
5) Convert
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W=,ffi
6)
the following angle measure from radians to degrees.Ztl/Ls
Find the le ngth of the a rc
(a
rc length) on a circle of radius 3 meters a nd interce pted by a centra
angle of 1"50".
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le
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7)
Find the radian measure )r
rf Ine
the cenu
r
ntra
length 7 feet,
I
a
ngre or a circre
:,^"1,':-{-7,)," pts
an arc
of
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6 fO
$r
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/4
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8)
ffi'bl?-t',
rei
Phonograph records are vinyl discs that rotate on a turntable. A typical
inches in diameter and plays at 33 1/3 revolutions per minute.
a) What is the angular speed of a record album?
b) What is the linear speed of the outer edge of a record album?
b)
rd album is 12
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9)
Find the area of the sectorof a circle of radius 6.5 millimeters and centralangle
ft= *r"*
k--
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t
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+a^Wn
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11) Evaluate (if possible
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srn(
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al
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=-F;g'i,lq
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tric functions at the given real number,
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t = -4n/3.
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Jc*4r l--ry
'-
^
J
A**rCl*ckbtt
I
t
=
sinlTr/4
5in tE t
-@
l"-
12) Evaluate the trigonometric function using its period as an aid.
r{
,iF
4./
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5'q
FE=-tr
h'-h
-A:{'ry
r,l'{'
;:
t='r
Q
y Tl . =PT
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*; tfut&r/n,^'[tZ )
10) Evaluate (if possible)
0
r%)= }i"p!+T
=js
n
,tr
e-
8O
-6{1
^4
t43
1-3) Evaluate the
trigonometric function using its period as an aid.
cos(-132l3)
-a)
dst
S,tn
tq ,5;^
/uq)
)=
=Si^/zztt{
Ssn
33=
?
15) Use the value of the trigonometric function to evaluate the indicated functions.
(t(t, f
sin(-r) = 3/B
a) sin t
b) csc t
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I
g
t3
Stng =
I
-tt'-
-2a
/
3
ff1:, C*H)= Cost ,[fl
t{\
1
lll["?,, Serk)r H ,zT-e=66,
16) Use the value of the trigonometric function to evalu ate the indicated functions.
\?y
COS
\,r
)' ot
c)
d)
cos(z+r]
.
\
Lt^
(^ (rr-t)= -'s
J*.
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[^(n+t)= -+
L7) Use a calculator to evaluate the trigonometric funct ion. Round your answer to four decimal
places. Make sure the mode in calculator is on radians.
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a) cscZrf3
b) cos (-1,7)
c)
cot (-0.9)
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2-
t{rndu,[oJ'n"ns
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18)
Find the exact values of the six trigonometric functions of the angle shown in the figure.
fuLo
=
{,7,'*
=i=ry
?i!y=*'ffi,
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#
,.
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I x
to*f'
,:_
6r(
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Lb
t41
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,fr
r:1, r
ff'r+= +=3
ffi
,t ktl > s,
;ff"8
x'fl
' yr>f= , rr7,2[L&o'i=iftl3 J)nt= = v
r
vat ue of the trigonometric fu nction to evaluate the indicated functions.
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=
tl
7
g=#,,{=T31,
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-lJ
1sCI=
,)*
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e,l-a19) usltne
r+/'
5rn
til3
t
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e
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r=
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20)
lfrl
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ofutfi/et{gonomelric function to evaluate the indicated
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Use the value
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yy,h i' ::i4,"-, oyq,y
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rr
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er-
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functions.
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b- l>2tl b
,/,
v
L
btn ff=
-r
2t)
h0= LI
f.Co5o
=A
Using the triangle above, verify/prove the following Pythagorean Trigonometric ldentity:
X"t?'= rL
sin20+ cos2e=7
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n)o
Ji^
r'
(r'coso)" l- (
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f'(os'? f fs;n's
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22)
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=
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Find the exact values of the six trigonometric ratios of the angle 0 in the given triangle.
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v'.t
WY
Y'+
Y', t{
1
f,no=N
fi0
fo}*:
-rr'-
r
G
1{v
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ws
ta
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u --
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cyft= M=
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r{
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w.
,kr
23l.
Find the exact values of the indicated variables.
5r,.. 4to=
tr, =
$in+t' : -!
0s ?r
u
28 S;notf,a=
x
1-.
h't0rn)'
Pt
=28
kLtr lf6't = Tttt
y'+ sq L -- 18'( I =
+ ry
P
x
-\
y
fr (ot?fo:
2t . tlAe* ^k
4
Sketch a triangle that has acute angle 0, and find the other five trigonometric ratios of 0.
a) cos0 = 9/40
b) tan1 = fi
c) cscO = 13/72
Cao
qX
' 4of
--l--
ar
4
quu';'(oL
Y 8t lf;lboa
lsn
uLl-,Y=,1st4
Art
n
X=,ffi
24)
Nf- k
-tse
(a /r', k
f, t,t,6-
k'= 3(
e7
ZV
25)
Evaluate the expression without using a calculator
sln30ocsc30o
a/
26)
LL
2;ft-l
7t
7 i.--J
a\
./
Evaluate the expression without using a calculator
(sin 60")2
*
(cos 60)2
($,+U)"
fru
27ll
*:1;n
Evaluate the expression without using a calculator
(l))L.,
6'" t;1'"'(;) - "'(1)'"'
.
rq
*-/4
L). 2- *
,')"
(@)
Gn qY=[+) '
7
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d-
4
q"
e
6-@=
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f-qls
=
betweenf,
pole is
the wire'and the ground is 52o. How far from the base of the: Pure
15 the
wrr tr dtLcrLIrtru
Lrr= wire
attached to
LU the
Lrrtr
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ground? Assume the pole is
t/a'
-lb
28) A guy wire runs from the ground to the top of a 25-foot telephone pole. The angle formed
lans)o'?
l^\u
=ffi
,'l
trx
^
-non-
=
ry-
i? X,ttnfio;9'{ }
/'/;2{
tln;?o
14,;Fr
29) A 20-ft ladder leans against a building so that the angle between the ground and the ladder is72'.
h
5in
1g,o
- -h
>o
2a,5ta ?)o
30)
uh
From a point on the gro u nd 500 ft from the base of the build ing, a n observer finds that the angle of
elevation to the top of the building is 24o and that the angle of elevation to the top of a flagpole
the height of the building and the length of the flagpole.
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