Download Fill in The Unit Circle

Practice: Lessons 4.7-4.8
Name:
Period:
Fill in The Unit Circle
Positive:
Positive:
e2ative:
(L
([0
Positive:
Nati ye:
LQiL)
Positive:
NJcgtti.
E meddedMh
co m
0
_________
______
1)
Evaluate the following without using a calculator. Use your unit circle.
a)
sin-1:]
d)
sin
(
1
O)
-n
_,1-
=
0
b)
sin’LLJ=
e)
=
1
SiflI—
c)
—
arcsin[_2-J
LE
I
1)
11
Lj
1
arcsin
——
itt
Tr
an
g)
cos
j)
cos(O)=
m)
arctan(1)
=
p)
arctan(O)
=
2)
Evaluate the following compositions of trigonometric functions using your unit circle:
(Remember: Evaluate the inside, and then solve the outside)
(0
h)
arccos(—1)=
k)
arccos
-rr
z
a)
n)
tanl(_1)=
q)
tan-’(\/)=
I)
cos_*/)=
cos cos
rr
o)
tan 1—1=
r)
tan
3
Tr
b)
=
=
sin[sin[_N]]
-yr
d)
cos’
f)
tan
h)
sin(sin
=
3
-
-rr
(
tan
3
Ltan___
1r
g)
=
3
(p
-
I——--=
alt
Lj
e)
JI
3
11
-
c)
3
COS’_=
rr
0
sin’(sinCllD]
D
(fl
-n
i)
0
(tan_i (o))=
0
(- i))=
Tt’
—
J
i)
COS
1
j)
(7
1(
cos cos—
=
—
1,
=
-rr
1i
11
k)
jJ
tan’( tan
1)
tan(tan’(_ i))= —
n)
sin sin
p)
cos
r)
tan(tan’(’J))= —
11
m)
sin
=
—
2
I.
o)
cos[cosu1_ij
q)
tan
2
=
[tan__IJ
=
—
-hi
3)
Find all of the missing sides and angles of the following triangles. Circle each final answer. Round
2 decimals places.
a)
B
b)
B
42
a
C
c
=
18
a
b =38
A
CoSA j
H4LI
A
cos(’
b
0
Sr S
I8
3D
2I°
EE’E
cZiEo
qO_O
8
qiq9
B
d)
c)
B
a
C
=10
a
b =30
IO 3D-C
443
A
12.
b=22
C
(00
-9-I
iW
CC’S
B
0
e)
c
=
B
25
a=12
c
C
i24
144
=32
a
b
Sr1 J2
A
C
b
+
I
CO
Co5O
—
3
a:
e.
_
coS
lao
)05
4)
Find the altitude of each of the following isosceles triangles. Round 2 decimals places.
30
30
12 feet
28 feet
k
3
-tn
—
ILl
(p
h
t,4an3r
b;
io;
/
78°
/k
8 feet
/oc9
lOfeet
h
SE
h
5)
s4cI°
Docking a boat
A boat is pulled in by means of a winch located on a dock 10 feet above the deck
of the boat. Let 0 be the angle of elevation from the boat to the winch. Find 0 if the length of the rope is
40 feet. Round 2 decimal places.
Sn@
9
/ %O
(ZEZEE°
Is.
6)
The sun is 32° above the horizon. Find the length of a shadow cast by a building that is 700 feet tall.
Round to the nearest foot.
a)
Draw a picture to represent the above situation
b
Find the length of the shadow.
700
-an3°:
x
I’
700
X
an32
4
x
(X
7)
The height of a tlagpole is 34 feet. You are standing 15 feet from the flagpole. What is the angle of
elevation from you to the top of the flagpole? Round to 2 decimal places.
a)
Draw a picture to represent the above situation.
b)
Find the angle of elevation.
onc
i
1
3L1
1
I s’
(q)