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MC
R3U
1-03
155
UN
IT5
TE
ST
:T
RIG
ON
OM
ET
RY
Mrs
.B
ehn
ke
Nam
e:__
____
____
____
____
____
____
___
PA
RT
A:
TR
IGO
NO
ME
TR
ICR
AT
IOS
.C
AS
TR
UL
EA
ND
SP
EC
IAL
TR
IAN
GL
ES
1.A
poin
tP(
3,-2
)lie
son
the
term
inal
arm
ofan
angl
eA
inst
anda
rdpo
siti
on.
(a)
Dra
wth
etr
iang
leon
the
(b)
Det
erm
ine
the
exac
tle
ngth
ofth
eC
arte
sian
Pla
ne.
[1]
term
inal
arm
(i.e
.Fi
ndr)
[1]
(b)
Sta
teth
e3
prim
ary
trig
onom
etri
cra
tios
infr
actio
nfo
rm(e
xact
answ
ers
—no
deci
mal
s).
[3]
(c)
Sta
teth
e3
reci
proc
altr
igon
omet
ric
rati
osin
frac
tion
form
.[3
]
(d)
Cal
cula
teth
ere
late
dac
ute
angl
e,/3
,an
dth
epr
inci
pal
angl
e,0
toth
ene
ares
tte
nth
ofa
deg
ree.
[2]
2.Fi
ndal
lva
lues
ofL
A,
toth
en
eare
stde
gree
if00
U36
0°.
For
full
mar
ks,
draw
adi
agra
mto
supp
ort
your
answ
ers.
[6]
a)co
sA=
_L
b)c
scO
=—
2
3.S
tate
two
valu
esof
Uto
the
nea
rest
degr
ee4.
Eva
luat
e.G
ive
anex
act
answ
er.
for
the
follo
win
gtr
igon
omet
ric
ratio
.[3
]Y
oum
ust
show
your
wor
kfo
rfu
llm
arks
.13]
cscO
=—
1.15
5co
s22S
°sin
4S°t
anl2
O°
5.U
seth
eC
AS
Tru
lean
dyo
urkn
owle
dge
ofsp
ecia
lan
gles
tode
term
ine
valu
esfo
ral
l3
prim
ary
trig
onom
etri
cra
tios
ofth
efo
llow
ing
angl
es.
For
full
mar
ks,
leav
ean
swer
sex
act
and
infr
actio
nfo
rman
dpr
ovid
ea
diag
ram
tosu
ppor
tyo
uran
swer
.[61
a)15
0°b)
315°
a.P
AR
TB
:A
PP
LIC
AT
ION
SO
FT
RIG
ON
OM
ET
RY
1.A
usti
n,B
enan
dC
eles
tear
esp
read
ou
tst
andi
ngin
afi
eld.
The
dist
ance
betw
een
Aus
tin
and
Cel
este
is7
m,
the
dist
ance
bet
wee
nA
usti
nan
dB
enis
9m
,Fr
omB
en’s
poin
tof
view
,th
eoth
ers
are
sep
arat
edby
anan
gle
of18
°.Fr
omC
eles
te’s
poin
tof
view
,by
wha
tan
gle
are
Aus
tinan
dB
ense
par
ated
?In
clud
ea
diag
ram
wit
hyo
urso
luti
on.
Ans
wer
toth
enea
rest
degr
ee.
[5]
2.T
hebu
oys
tom
ark
the
tria
ngul
arco
urse
for
aya
cht
race
are
loca
ted
atpo
ints
V.T,
and
C.
IfY
T=
3.5
km
,<
Y=
65°,
and
<T
=71
°,det
erm
ine
the
tota
lle
ngth
ofth
eco
urse
,co
rrec
t
toon
ede
cim
alpl
ace.
[51
K
3.D
eter
min
eth
eva
lue
ofan
gle
9,to
the
near
est
degr
ee.
NO
TE:
The
diag
ram
isN
OT
tosc
ale.
[5]
5N
L6.
2cm
M
PA
RT
C:
TR
IGO
NO
ME
TR
ICID
EN
TIT
IES
(121
For
the
follo
win
gqu
esti
ons,
prov
eO
NL
Y3
ofth
e5
trig
onom
etri
cid
entit
ies.
Be
sure
tost
ate
whi
chid
enti
tyw
asu
sed
.E
ach
proo
fis
out
of4
for
ato
tal
of12
mar
ks.
Tw
obo
nus
mar
ksw
illbe
awar
ded
ifyo
uan
swer
all
five
.©
Pla
cea
chec
kmar
kin
the
corn
erof
the
proo
fsyo
uw
ant
mar
ked
out
of4.
cosS
=si
nfi
cotO
[
sec2
O+
csc2
8=
sec2
Ocs
c2fl
cos2
O—
cos4
O=
cos2
Osi
n2O
Ess
enti
alSk
ills:
sinG
=cs
cU(1
+co
sO)
1—
cos9
cotO
—ta
nS
=si
no+c
o.5e
csc8
—se
cO
[1S
alve
prob
lem
sus
ing
the
Sine
Law
(obl
ique
tria
ngle
s)U
Solv
epr
oble
ms
usin
gth
eC
osin
eLa
w(o
bliq
uetr
iang
les)
CD
eter
min
em
easu
res
intr
iang
les
invo
lvin
gth
eam
bigu
ous
case
ofth
eSi
neL
aw
oG
iven
anan
gle,
dete
rmin
etr
igon
omet
ric
rati
osus
ing
spec
ial
tria
ngle
san
dC
AST
rule
-G
iven
atr
igon
omet
ric
rati
o,de
term
ine
two
prin
cipa
lan
gles
usin
gsp
ecia
ltr
iang
les
and
CA
STru
leU
Prov
esi
mpl
etr
igon
omet
ric
iden
titi
es(i
nvol
ving
PI,
QIR
I)
Mar
kth
isout
of4?
C‘I
IMark
this
outo
f4?
IM
arkth
isou
tof
4?C
Mar
kth
isou
tof
4?0
Mar
kth
isout
of4?
0
1-
4.
a
MC
R3U
1-04
155
UN
IT5
TE
ST
:T
RIG
ON
OM
ET
RY
Mrs
.B
ehn
ke
Nam
e:__
____
____
____
____
____
____
____
PA
RT
A:
TR
IGO
NO
ME
TR
ICR
AT
IOS
.C
AS
TR
UL
EA
ND
SP
EC
IAL
TR
IAN
GL
ES
1.A
poin
tP(
2,-5
)lie
son
the
term
inal
arm
ofan
angl
e9
inst
anda
rdpo
sitio
n.(a
)D
raw
the
tria
ngle
onth
e(b
)D
eter
min
eth
eex
act
leng
thof
the
Car
tesi
anP
lane
.[1
]te
rmin
alar
m(i
.e.
Find
r)[1
]
(c)
Sta
teth
e3
prim
ary
trig
onom
etri
cra
tios
infr
actio
nfo
rm(e
xact
answ
ers
—no
deci
mal
s).
[31
(d)
Sta
teth
e3
reci
proc
altr
igon
omet
ric
rati
osin
frac
tion
form
.[3
]
(e)
Cal
cula
teth
ere
late
dac
ute
angl
e,/3
,an
dth
epr
inci
pal
angl
e,9
toth
enea
rest
tent
hof
ade
gree
.[2
1
2.Fi
ndal
lva
lues
ofto
,to
the
nea
rest
degr
eeif
09
3600
.F
orfu
llm
arks
,dr
awa
diag
ram
tosu
ppor
tyo
uran
swer
s.[6
]-1
a)sr
nfl
=çj
=b)c
scO
=p
3.S
tate
two
valu
esof
0to
the
nea
rest
degr
ee4.
Eva
luat
e.G
ive
anex
act
answ
er.
for
the
follo
win
gtr
igon
omet
ric
ratio
.[3
]Y
oum
ust
show
your
wor
kfo
rfu
llm
arks
.[3
]se
cO=
—1.
155
cos3
O°s
in3l
S°t
anlS
O°
4.U
seth
eC
AS
Tru
lean
dyo
urkn
owle
dge
ofsp
ecia
lan
gles
tode
term
ine
valu
esfo
ral
l3
prim
ary
trig
onom
etri
cra
tios
ofth
efo
llow
ing
angl
es.
For
full
mar
ks,
leav
ean
swer
sex
act
and
infr
actio
nfo
rman
dpr
ovid
ea
diag
ram
tosu
ppor
tyo
uran
swer
.16
1
a)22
5°b)
330°
PA
RT
B:
AP
PL
ICA
TIO
NS
OF
TR
IGO
NO
ME
TR
Y
1.A
ustin
,B
enan
dC
eles
tear
esp
read
out,
stan
ding
inaf
ield
.T
hedi
stan
cebe
twee
nA
ustin
and
Cel
este
is7
m,
the
dist
ance
betw
een
Aus
tinan
dB
enis
9m
,Fr
omB
en’s
poin
tof
view
,th
eot
hers
are
sep
arat
edby
anan
gle
of18
°.Fr
omC
eles
te’s
poin
tof
view
,by
wha
tan
gle
are
Aus
tinan
dB
ense
par
ated
?In
clud
ea
diag
ram
with
your
solu
tion
.A
nsw
erto
the
nea
rest
degr
ee.
151
2.T
wo
buil
ding
sar
ese
par
ated
byan
alle
yway
that
is21
met
res
wid
e.T
hedi
stan
cefr
omth
eto
pof
the
shor
ter
build
ing
toth
eto
pof
the
tall
erbu
ildin
gis
35m
etre
s.T
hean
gle
ofde
pres
sion
from
the
top
ofth
esh
orte
rbu
ildin
gto
the
bott
omof
the
tall
erbu
ildin
gis
500.
Wha
tis
the
heig
htof
the
talle
rbu
ildin
gto
the
nea
rest
met
re?
Incl
ude
adi
agra
mw
ithyo
urso
luti
on.
[5]
3.D
eter
min
eth
eva
lue
ofan
gle
9,to
the
nea
rest
degr
ee.
NO
TE:T
hedi
agra
mis
NO
Tto
scal
e.[5
]
I
N
K
5.9
6.2
cmM
PA
RT
C:
TR
IGO
NO
ME
TR
ICID
EN
TIT
IES
1121
For
the
follo
win
gqu
esti
ons,
pro
ve
ON
LY
3of
the
5tr
igon
omet
ric
iden
titi
es.
Be
sure
tost
ate
whi
chid
enti
tyw
asuse
d.
Eac
hpr
oof
isou
tof
4fo
ra
tota
lof
12m
arks
.T
wo
bonu
sm
arks
will
beaw
arde
dif
you
answ
eral
lfi
ve.
©P
lace
ach
eckm
ark
inth
eco
rner
ofth
epr
oofs
you
wan
tm
arke
dou
tof
4.
cscO
=se
c6co
t8M
ark
this
out
of4?
ci
cosU
+si
n20
=se
c9M
ark
this
out
of4?
cico
sO
Ess
enti
alS
kill
s:U
Solv
epr
oble
ms
usin
gth
eSi
neLa
w(o
bliq
uetr
iang
les)
US
alve
prob
lem
sus
ing
the
Cos
ine
Law
(obl
ique
tria
ngle
s)U
Det
erm
ine
mea
sure
sin
tria
ngle
sin
volv
ing
the
ambi
guou
sca
seof
the
Sine
Law
oG
iven
anan
gle,
dete
rmin
etr
igon
omet
ric
rati
osus
ing
spec
ial
tria
ngle
san
dC
AST
rule
0G
iven
atr
igon
omet
ric
rati
o,de
term
ine
two
prin
cipa
lan
gles
usin
gsp
ecia
ltr
iang
les
and
CA
STru
leo
Prov
esi
mpl
etr
igon
omet
ric
iden
titi
es(i
nvol
ving
PIQ
I.R
I)
IMark
this
outo
f4?U
I(s
inO
—co
sO)(
sinO
+co
sO)z
.%
5inS
—I
tan
S+
cotS
=se
c8cs
cS.
Mar
kth
isout
of4?
tan
S—
sinS
secf
l=
Mar
kth
iso
ut
of4?
cisi
n3S
1+
cosO
MC
R3U
l-05
/55
UN
ITS
TE
ST
:T
RIG
ON
OM
ET
RY
Mrs
.R
ehn
ke
Nam
e:__
____
____
____
____
____
____
____
PA
RT
A:
TR
IGO
NO
ME
TR
ICR
AT
IOS
.C
AS
TR
UL
EA
ND
SP
EC
IAL
TR
IAN
GL
ES
1.A
poin
tP(
-5,
-2)
lies
onth
ete
rmin
alar
mof
anan
gle
8in
stan
dard
posi
tion
.(a
)D
raw
the
tria
ngle
onth
e(b
)D
eter
min
eth
eex
act
leng
thof
the
Car
tesi
anP
lane
.[1
]te
rmin
alar
m(i
.e.
Find
r)[1
]
(c)
Sta
teth
e3
prim
ary
trig
onom
etri
cra
tios
infr
actio
nfo
rm(e
xact
answ
ers
—no
deci
mal
s).
[3]
(d)
Sta
teth
e3
reci
proc
altr
igon
omet
ric
rati
osin
frac
tion
form
.[3
]
(e)
Cal
cula
teth
ere
late
dac
ute
angl
e,41
, and
the
prin
cipa
lan
gle,
9to
the
near
est
tent
hof
adeg
ree.
[2]
2.Fi
ndal
lva
lues
oftO
,to
the
nea
rest
degr
eeif
0°9
360°
.F
orfu
llm
arks
,dr
awa
diag
ram
tosu
ppor
tyo
uran
swer
s.[6
]a)
cosO
=5
b)c
ot8
=q
’
3.S
tate
two
valu
esof
Uto
the
nea
rest
degr
ee4.
Eva
luat
e.G
ive
anex
act
answ
er.
for
the
follo
win
gtr
igon
omet
ric
ratio
.I]
You
mus
tsh
owyo
urw
ork
for
full
mar
ks.
I]ta
nfl
=0.
777
cosS
lS°s
in3O
°tan
l2O
°
4.U
seth
eC
AST
rule
and
your
know
ledg
eof
spec
ial
angl
esto
dete
rmin
eva
lues
for
all
3pr
imar
ytr
igon
omet
ric
rati
osof
the
follo
win
gan
gles
.F
orfu
llm
arks
,le
ave
answ
ers
exac
t and
infr
actio
nfo
rman
dpr
ovid
ea
diag
ram
tosu
ppor
tyo
uran
swer
.[6
]
a)22
5°b)
330°
PA
RT
B:
APP
LIC
AT
ION
SO
FT
RIG
ON
OM
ET
RY
1.A
fore
stra
nger
spot
sa
fire
ona
bear
ing
of02
00fr
omhe
rst
atio
n.Sh
ees
tim
ates
that
the
fire
isab
ou
t10
kmaw
ay.
Ase
cond
stat
ion
isdu
eea
stof
the
firs
t.A
rang
erin
the
seco
nd
stat
ion
thin
ksth
atth
efi
reis
about
12km
away
from
him
.H
owfa
rap
art
are
the
two
stat
ions
,to
the
nea
rest
kilo
met
re.
[5]
2.T
hebu
oys
tom
ark
the
tria
ngul
arco
urse
for
aya
cht
race
are
loca
ted
atpo
ints
Y,T,
and
C.If
y=
3.5
km,
t=
5.8
km,a
ndL
Y=
M,d
eter
min
eth
eto
tal
lene
th-o
fth
cco
urse
,35
fj1
.eo’
afl
QC
-C-
corr
ect
toon
ede
cim
alpl
ace.
[5]
-‘
3.D
eter
min
eth
eva
lue
ofan
gle
e,to
the
near
est
degr
ee.
NO
TE:
The
diag
ram
isN
OT
tosc
ale.
[5]
10 m
9.8
m
PA
RT
C:
TR
IGO
NO
ME
TR
ICID
EN
TIT
IES
1127
For
the
follo
win
gqu
esti
ons1
pro
ve
ON
LY
3of
the
5tr
igon
omet
ric
iden
titi
es.
Be
sure
tost
ate
whi
chid
enti
tyw
asu
sed
.E
ach
proo
fis
out
of4
for
ato
tal
of12
mar
ks.
Tw
obo
nus
mar
ksw
illbe
awar
ded
ifyo
uan
swer
all
five
.©
Pla
cea
chec
kmar
kin
the
corn
erof
the
proo
fsyo
uw
ant
mar
ked
out
of4.
secO
=cs
cOta
n8M
ark
this
out
of4?
H
Ess
enti
alSk
ills:
Mar
kth
isou
tof
4?0
9So
lve
prob
lem
sus
ing
the
Sine
Law
(obl
ique
tria
ngle
s)U
Solv
epr
oble
ms
usin
gth
eC
osin
eLa
w(o
bliq
uetr
iang
les)
JD
eter
min
em
easu
res
intr
iang
les
invo
lvin
gth
eam
bigu
ous
case
ofth
eSi
neLa
w
Mar
kth
isout
of4?
0
tanf
i—
cotO
=si
n6-j
-cG
Mark
this
ou
tof4
?H
secO
—cs
cO
Giv
enan
angl
e,de
term
ine
trig
onom
etri
cra
tios
usin
gsp
ecia
ltr
iang
les
and
CA
STru
le-
Giv
ena
trig
onom
etri
cra
tio,
dete
rmin
etw
opr
inci
pal
angl
esus
ing
spec
ial
tria
ngle
san
dC
AST
rule
UPr
ove
sim
ple
trig
onom
etri
cid
enti
ties
(invo
lvin
gP
r,Q
I.R
I)
cos8
(sec
6—
1)=
1—
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(sin
S—
cosU
)2=
1—
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Oco
sS
cos2
9
1+
sin
9=
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sin
SIM
ark
this
outo
f4?
0
MC
R3U
l-03
UN
IT5
TE
ST
:T
RIG
ON
OM
ET
RY
IM
rs.
Beh
nk
eN
ame:
/3Q
ffrn
PA
RT
A:
TR
IGO
NO
ME
TR
ICR
AT
IOS
.C
AS
TR
UL
EA
ND
SP
EC
IAL
TR
IAN
GL
ES
1.A
poin
tP(
3,-2
)lie
son
the
term
inal
arm
ofan
angl
eU
inst
anda
rdpo
sitio
n.(a
)D
raw
the
tria
ngle
onth
eC
arte
sian
Pla
ne.
[1]
&(c
)S
tate
the
3re
cipr
ocal
csc
3.S
tate
two
valu
esof
Uto
the
nea
rest
degr
eefo
rth
efo
llow
ing
trig
onom
etri
cra
tio.
[3]
cscf
l=
—1.
155
(b)
Det
erm
ine
the
exac
tle
ngth
ofth
ete
rmin
alar
m(i
.e.
Find
r)[1
]
4ctn
G_
-z
—3
trig
onom
etri
cra
tios
infr
actio
nfo
rm.
[1
3
Co*&
a
2-
5.U
seth
eC
AS
Tru
lean
dyo
urkn
owle
dge
ofsp
ecia
lan
gles
tode
term
ine
valu
esfo
ral
l3
prim
ary
trig
onom
etri
cra
tios
ofth
efo
llow
ing
angl
es.
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mar
ks,
leav
ean
swer
sex
act
and
infr
actio
nfo
rman
dpr
ovid
ea
diag
ram
tosu
ppor
tyo
uran
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.[6
]
ccso
4.i
3I5
°
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is= tz-f
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e3
prim
ary
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onom
etri
cra
tios
infr
actio
nfo
rm(e
xact
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ers
—no
deci
mal
s).
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os9
v
a)cosA
=7=
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Cal
cula
teth
ere
late
dac
ute
angl
e./1
,an
dth
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inci
pal
angl
e,S
toth
enea
rest
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ree.
[2]
t E33.1
2.Fi
ndal
lva
lues
ofto
,to
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nea
rest
degr
eeif
00
836
0°.
For
full
mar
ks,
draw
adi
agra
mto
supp
ort
your
answ
ers.
[61
1b)c
scO
=—
2
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0
oc
330
4.E
valu
ate.
Giv
ean
exac
tan
swer
.Y
oum
ust
show
your
wor
kfo
rfu
llm
arks
.[3
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sZ2S
°sin
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anl2
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=—
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_vi
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/
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O’
-ai
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rC
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°t3
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—
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3°
n32’
—‘
——
5—
Z
ci
a
PA
RT
B:
AP
PL
ICA
TIO
NS
OF
TR
IGO
NO
ME
TR
Y
1.A
usti
n,B
enan
dC
eles
tear
esp
read
out,
stan
ding
ina
fiel
d.T
hedi
stan
cebet
wee
nA
ustin
and
Cel
este
is7
m,
the
dist
ance
bet
wee
nA
ustin
and
Ben
is9
m,
From
Ben
’spo
int
ofvi
ew,
the
oth
ers
are
sep
arat
edby
anan
gle
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°.Fr
omC
eles
te’s
poin
tof
view
,by
wha
tan
gle
are
Aus
tinan
dB
ense
par
ated
?In
clud
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diag
ram
wit
hyo
urso
luti
on.
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wer
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enea
rest
degr
ee.
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9-7
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.
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=3.
a_
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ram
isN
OT
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,5q
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}/o
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7
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hebu
oys
tom
ark
the
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ngul
arco
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aya
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ted
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Y=
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°,det
erm
ine
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lle
ngth
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C
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ET
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ITIE
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rth
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ques
tion
s,pro
ve
ON
LY
3of
the
5tr
igon
omet
ric
iden
titi
es.
Be
sure
tost
ate
whi
chid
enti
tyw
asu
sed
.E
ach
proo
fis
out
of4
for
ato
tal
of12
mar
ks.
Tw
obo
nus
mar
ksw
illbe
awar
ded
ifyo
uan
swer
all
five
.©
Pla
cea
chec
kmar
kin
the
corn
erof
the
proo
fsyo
uw
ant
mar
ked
out
of4.
cosU
=si
nOco
tO
CM
ark
this
out
of4?
0
snQ
,cçS
QC
°‘‘
ifl&
-
coa9
—
___
—
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knO
Ess
enti
alSk
ills:
oSo
lve
prob
lem
sus
ing
the
Sine
Law
(obl
ique
tria
ngle
s)o
Solv
epr
oble
ms
usin
gth
eC
osin
eLa
w(o
bliq
uetr
iang
les)
UD
eter
min
em
easu
res
intr
iang
les
invo
lvin
gth
eam
bigu
ous
caseo
fth
eSi
neLa
w
EG
iven
anan
gle,
dete
rmin
etr
igon
omet
ric
rati
osus
ing
spec
ial
tria
ngle
san
dC
AS
Tru
leo
Giv
ena
trig
onom
etri
cra
tio,
dete
rmin
etw
opr
inci
pal
angl
esus
ing
spec
ial
tria
ngle
san
dC
AS
Tru
le
Mar
kth
isout
of4
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sec2
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O=
sec2
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c2O
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SS
n-&
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=cs
cO(1
+co
sS)
this
outo
f 4?
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sinS
1—
cosS
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sG\—
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(
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0
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O=
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Osi
n26
—
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&C
s\n
—
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—
t
—
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NC
-çne
(z)5
e)t”
( LoknG
ccS
OJ I
-C
co(4i4
CcV
UPr
ove
sim
ple
trig
onom
etri
cid
enti
ties
(invo
lvin
gP
T,Q
IJI)
MC
R3U
1-04
--
-15
5U
NIT
ST
ES
T:
TR
IGO
NO
ME
TR
YM
rs.
Beh
nke
Nam
e:__
____
____
____
_
PA
RT
A:
TR
IGO
NO
ME
TR
ICR
AT
IOS.
CA
ST
RU
LE
AN
DS
PE
CIA
LT
RIA
NG
LE
S
—t3
t:
1c’C
C
&t5
o° 0
0
\5O
Ot
liD
r=4
A+
9
r=
T
& G 4.
Eva
luat
e.G
ive
anex
act
answ
er.
You
mus
tsh
owyo
urw
ork
for
full
mar
ks.
[3]
co
s3o
°sin
3lS
°tan
lSO
’
‘j-
(zsns(
4&n0
j
4.U
seth
eC
AST
rule
and
your
know
ledg
eof
spec
ial
angl
esto
dete
rmin
eva
lues
for
all
3pr
imar
ytr
igon
omet
ric
rati
osof
the
follo
win
gan
gles
.F
orfu
llm
arks
,le
ave
answ
ers
exac
tand
infr
actio
nfo
rman
dpr
ovid
ea
diag
ram
tosu
ppor
tyo
uran
swer
.[6
]
—I
7-
Caa
——
cost
i
C>
/z
(c)
Sta
teth
e3
deci
mal
s).
Lt
1.A
poin
tP(
2,-5
)lie
son
the
term
inal
arm
ofan
angl
eei
nst
anda
rdpo
siti
on.
(a)
Dra
wth
etr
iang
leon
the
(b)
Det
erm
ine
the
exac
tle
ngth
ofth
eC
arte
sian
Pla
ne.
[1]
term
inal
arm
(i.e
.Fi
ndr)
[1]
prim
ary
trig
onom
etri
cra
tios
infr
actio
nfo
rm(e
xact
answ
ers
—no
[3]
a
Q(d
)S
tate
the
3re
cipr
ocal
trig
onom
etri
cra
tios
infr
actio
nfo
rm.
[3]
csc&
-J
5
(e)
Cal
cula
teth
ere
late
dac
ute
angl
e,/3
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dth
epr
inci
pal
angl
e,0
toth
ene
ares
tte
nth
ofa
degr
ee.
[2]
2.Fi
ndal
lva
lues
oftO
,to
the
nea
rest
degr
eeif
00
036
0°.
For
full
mar
ks,
draw
adi
agra
mto
supp
ort
your
answ
ers.
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0=
5
Vv0
3.S
tate
two
valu
esof
8to
the
nea
rest
degr
eefo
rth
efo
llow
ing
trig
onom
etri
cra
tio.
[3]
sec8
=—
1.15
5
I” /
a)22
5°
/
b)csc8=
()L
5.3
sflc
.iv.
c)
ci
0
oR
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b)33
0°3
°/
4a.i
Z25
0
=1
51
037
Q0
cos33°
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00
cc,s
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in3O
4
L-
i2_3
b
PA
RT
B:
APP
LIC
AT
ION
SO
FT
RIG
ON
OM
ET
RY
1.A
ustin
,B
enan
dC
eles
tear
esp
read
out,
stan
ding
inaf
ield
.T
hedi
stan
cebe
twee
nA
ustin
and
Cel
este
is7
m,
the
dist
ance
betw
een
Aus
tinan
dB
enis
9m
,Fr
omB
en’s
poin
tof
view
,th
eot
hers
are
separ
ated
byan
angl
eof
18°.
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Cel
este
’spo
int
ofvi
ew,
byw
hat
angl
ear
eA
ustin
and
Ben
separ
ated
?In
clud
ea
diag
ram
with
your
solu
tion
.A
nsw
erto
the
nea
rest
degr
ee.
[5]
-7.
I57
°
It
%1.
1sajeei4iter
rp
o
a3°
7op0
2.T
wo
buil
ding
sar
ese
par
ated
byan
all
esa
yth
atis
21m
etre
sw
ide.
The
dist
ance
from
the
top
ofth
esh
orte
rbu
ildin
gto
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top
ofth
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ller
build
ing
is35
met
res.
The
angl
eof
depr
essi
onfr
omth
eto
pof
the
shor
ter
build
ing
toth
ebo
ttom
ofth
eta
ller
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ing
is50
°.W
hat
isth
ehe
ight
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eta
ller
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ing
toth
en
eare
stm
etre
?In
clud
ea
diag
ram
with
your
solu
tion
.[5
]
W11
3’—
2
99.
-
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1je
L{4J
bda-
kn93
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c;m
aK
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I-
3.D
eter
min
eth
eva
lue
ofan
gle
0,to
the
nea
rest
degr
ee.
NO
TE:T
hedi
agra
mis
NO
Tto
scal
e.[51
a%
-i-(,cj)
ftz
)cosH
9’Z
MIl
ci
y4
1q
5”7
2(1
.i
6.2
cmM
22
-—
flcosN
CCXD
tfl,
&o
LIz
..I
--
o.V
111
‘-
- —
hi
N—
PA
RT
C:
TR
IGO
NO
ME
TR
ICID
EN
TIT
IES
1121
For
the
follo
win
gqu
esti
ons,
pro
ve
ON
LY
3of
the
5tr
igon
omet
ric
iden
titie
s.B
esu
reto
stat
ew
hich
iden
tity
was
use
d.
Eac
hpr
oof
isou
tof
4fo
ra
tota
lof
12m
arks
.T
wo
bonu
sm
arks
will
beaw
arde
dif
you
answ
eral
lfi
ve.
©P
lace
ach
eckm
ark
inth
eco
rner
ofth
epr
oofs
you
wan
tm
arke
dou
tof
4.
csc8
=se
c8co
tOM
ark
this
out
of4?
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kC
o
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&co
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s’c
C)
sin2
Bco
sO+
=se
cOM
ark
this
out
of4?
CM
ark
this
out
of4?
Lico
sU(s
inS
—co
sB)(
sinO
+co
sO)
—uif
lcC
OS
CO
S-,\
(-i
tanS
+co
tO=
secO
cscf
lta
nS
—si
nS
secO
Mar
kth
isou
tof
4?LI
=M
ark
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tzin
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—se-c
ecos&
U+
ccss)
____
__
__
___
__
__
__
__
__
__
_______
14-C
DS
&
Ess
enti
alSk
ills:
US
olve
prob
lem
sus
ing
the
Sin
eLo
w(o
bliq
uetr
iang
les)
Giv
enan
angl
e,det
erm
ine
trig
onom
etri
cra
tio
sus
ing
spec
ial
rS
olve
prob
lem
sus
ing
the
Cos
ine
Law
(obl
ique
tria
ngle
s)tr
iang
les
and
CA
STru
le
zD
eter
min
em
easu
res
intr
iang
les
invo
lvin
gth
eU
Giv
ena
trig
onom
etri
cra
tio,
det
erm
ine
two
prin
cipa
lan
gles
ambi
guou
sca
seof
the
Sin
eLa
wus
ing
spec
ial
tria
ngle
san
dC
AST
rule
UPr
ove
sim
ple
trig
onom
etri
cid
enti
ties
(inv
olvi
ngP
I,Q
I.R
I)
MC
R3U
1-05
155
UN
ITS
TE
ST
:T
RIG
ON
OM
ET
RY
Mrs
.B
ehnke
Nam
e:__
____
____
____
_
PA
RT
A:
TR
IGO
NO
ME
TR
ICR
AT
IOS.
CA
ST
RU
LE
AN
DSP
EC
IAL
TR
IAN
GL
ES
1.A
poin
tP(
-5,
-2)
lies
onth
ete
rmin
alar
mof
(a)
Dra
wth
etr
iang
leon
the
Car
tesi
anP
lane
.[1
]
anan
gIe
0in
stan
dard
posi
tion
.(b
)D
eter
min
eth
eex
act
leng
thof
the
term
inal
arm
(i.e
.Fi
ndr)
[1]
r=,j
a9
5
(d)
Sta
teth
e3
reci
proc
altr
igon
omet
ric
rati
osin
frac
tion
form
.[3
]
cscO
-*L
S2-
(e)
Cal
cula
teth
ere
late
dac
ute
angl
e,/3
,an
dth
epr
inci
pal
angl
e,9
toth
enea
rest
tent
hof
ade
gree
.[2
]
1ti
r’(O
,’&-
=:\c
go\
o
2.Fi
ndal
lva
lues
ofto
,to
the
nea
rest
degr
eeif
0°U
3600
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orfu
llm
arks
,dr
awa
diag
ram
tosu
ppor
tyo
uran
swer
s.[6
]a)
cosO
=frzq5°iZ
V
for
the
follo
win
gtr
igon
omet
ric
ratio
.[3
]ta
nO= 0
.777
0
b)c
otf
l=j
01an3_
oR
.
V4.
Eva
luat
e.G
ive
anex
act
answ
er.
You
mus
tsh
owyo
urw
ork
for
full
mar
ks.
[3]
co
s3lS
°sin
3O
°tan
l2O
°
cocS
in3°
-
0
4.U
seth
eC
AS
Tru
lean
dyo
urkn
owle
dge
ofsp
ecia
lan
gles
tode
term
ine
valu
esfo
ral
l3
prim
ary
trig
onom
etri
cra
tios
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