Summer 2012
July 9, 2012
Math 1060-003
Midterm #2
Midterm #2: Trigonometric Functions
Instructions: You may use a calculator to assist you with any arithmetic, a writing
utensil, and your 3x5 reference card that you have prepared. No other materials
are permitted. You may circle ONLY one answer choice for each question. If
more than one answer choice is circled, it will be recorded as incorrect. The
point value of each problem is specified next to the problem statement. You may
turn in your exam and leave when you have finished.
Recommendation: You do not need to work on these problems in order. I would
suggest first answering the ones you find the easiest. Then go back and work on
the harder ones at the end. Also, if you finish early I would suggest double
checking all of your work, just in case you made any very simple mistakes.
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Summer 2012
July 9, 2012
Math 1060-003
Midterm 142
1
Which of the following angles is a solution to sin
1.
(a)
() ?
300
ç(jiO)
(c) 150°
(d) 300°
(e) 330°
An air plane is flying with an altitude of 5km. It can see a building on fire when looking
2.
angle
of depression of 15°. What is the distance between the airplane and the building?
at an
(a)
(b)
(c)
(d)
1.34 km
5.17 km
18.66 km
19.32 km
-
5k
-
Svii5j
tL Vv
)t
ic) 3
1
1
i?j
Given that tan(O)
3.
=
2 and 0 is inuadrant Ill, what is sin (8)?
I
(a)
b
()
(c)
5Y_ze
—
-
5
2
(
5-
--
q
5—
21
(
(e)
c
3f
•-‘
.)rn t”
——
S
I
— —vg
g4
2
QItt
—9
8) —1)
(9)(sec
cos
(
Which of the following expressions is equivalent to 2
4.
(a)
(b)
(c)
(d)
‘e
0)
tan
(
2
tan(0)
(8)
2
cos
cos(8)
O
2
sin
CS2(2c
-
—
CSL
/L
k
c.)Sg
—()
oR
(oS(
—)
2
c
1
Summer 2012
July 9, 2012
Math 1060-003
Midterm #2
Which of the following equations is true?
5.
(a)
(b)
sec(x)+1
=
—
(c) csc(x)
(d)
sin(x)
cos(x) +
sin(x)
+
=
1
csc (x)
— sin(x)
=
cos(x)
cs()
cc()
—
cos(x) cot (x)
cot(x)
(‘.)()
çqy)
5jV)[c)
=
-
(e) cos(_x) =sec(x)
I
i—
6.
(x) —4
2
Find all values of x in the interval {0,2ir] that satisfy the equation 3 sec
(a) x
it
it
it
(c) x
(d) x
5ir
57r
2rr
6
2ir
=
it
it
x)
3sc
(
t
•1
0
r
2:-
x)
SeL
(
2
2ir
-J
=
—
it
5ir 7ir hit
it
2it 47r 5rr
Given that sin(x)
_1—_’
A_:
—
t—
‘.
Cos(x)
=
(e) x=,—,--,-
7.
q
=
.
J
I’,
.—
/
‘‘
c.s (x)
=
and cos(y)
=
—
find cos (x + y). Assume that x is in
Quadrant I and y is in Quadrant II.
c()S()- s(i)ci(y)
16
(a) —
—
Lc)
/- )&
s
2/
—-—
(C)-!
ç4)
cz()
3
sz.y}k c
.)r;qJ)
I
(i)
8.
():
-
Find all x on the interval [O,2rr] that solve the equation sin(2x)
cos (x).
ir3irirrr
(a) x
=
(b) x
=
2
2
4’
4
0,ir,2ir
ir 5yr
(c) x
/
ir Sir
b
—,,—,—,—
2 4
ir 2ir
4
r 5ir
5m
(d) x 0,—,--,ir
(e)/
=
it
=
:;w9
9in
(zr)
(x)
coct) O
cjc(ij
CJS&)
0
:j
/\-
7;] -l
Summer 2012
July 9, 2012
Math 1060-003
Midterm #2
x)?
sin
(
x) 2
cos
(
Which of the is equivalent to 2
9.
ç’(x (I-(I
cZ()
(a) sin (4x)
±cs(2x)
(b)!cos(2x)+cos (4x)
/(c)
is...
——cos (4x) _)
—
8
8
(e) 1
—
cos(2x) + cos (4x)
lfcos(x) =!thenwhatiscos
10.
(a)—
(b)
(c)
(d)
i
(e)
11.
9
(Assume x is in Qi).
(5c
5
2
1
-
c(LX cI
—
—
5
(J5_ j)
—
13
B
Given a triangle with
= 500
5, find c?
and a
cC
(b) 7.66
(c) 2.54
(d) 3.26
(e)1.71
s0)
C 9’
C-’
5co)
c
12.
z-
Given a triangle with A
=
30°, a
(a) None
(b)One
c) Tvà>
(d) tfree
(e) Not enough information is given
S
=
10 and b
=
15, how many solutions are possible?
(--
c
Ic)
)Ly
13
r
)2’ c ci’ (c
k
I
dO
Summer 2012
July 9, 2012
Math 1060-003
Midterm #2
Alice sees a tall mountain in the distance. From where she is standing she needs to look
13.
up at an angle of 30° to see the peak. Bob is standing 1,000 feet behind Alice and needs to look
up at an angle of 28° to see the peak. How tall is the mountain?
-I)
(b)
(c)
(d)
(e)
6,726
5,419
4,621
3,917
2,152
L
//
feet
feet
feet
feet
k
jt?
h
(
LV1
fet’
(1
-
(2)
(t ) tci (2)
h
k
ct
j(J+iL)
,l3))
(x)
2
Find all solutions of the equation sin
14.
(a)
jr
3ir
=
—
(b) 0,m,2ir
(c)
ir
5ir
—
—
ir
57r
6’ 6
7m
‘
‘,f
z
1171
6 ‘ 6
371
(e) 0,,ir,—,2ir
Given that tan(x)
15.
=
3, find cos (2x). Assume that x is in Ui.
(S(2)
(a)
(b)
(c)
I
sJ1x)
-.
—
d)
10
1x)—
)O
(
L
ccZfr)
I
Syl()
Lq
To
Z(y)
(e)7
./3o)
0 on the interval [0,2ir].
I
=
—,—
j,Lj7
cH