Math 1060-003
Midterm #1
Summer 2012
June 11, 2012
Midterm #1: 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.
Name:______________________
Summer 2012
June 11, 2012
Math 1060-003
Midterm #1
Which of the following is co-terminal with a 4200 angle?
1.
a
Cad
(b)
--j
3
j0
(c)—
2.
/
fl7
(d) 3ir
(e) 420ir
Li
3
3
2 (45°)
45°) + tan
cos
(
45°) + 2
sin
(
Evaluate the following: 2
=
?
\t
(a) 0
(b) 1
(c) 2
(d)3
(e) 4
3.
°)
s
/
2
ca(s)
I
ccs)
In which quadrant is U if tan(O) > 0 and sec(O) < 0?
(a) Quadrant I
(b) Quadrant II
(c)QuadrantIIIJ
(d) Quadrant IV
(e) It cannot be determined.
>
Sc
<
0
LL
A cake of radius 6 inches is cut so that each s ice has a central angle of 60°. What is the
4.
area of one slice of cake?
(a) 1080 square inches
(b) 360 square inches
3
2
(c 2ir sQuare inches
(d) 6Tsquareinc
(e) 36ir square inches
i-1 ii
=
2
3
I
-
3
2
Summer 2012
Math 1060-003
Midterm #1
Given that sin(O)
5.
June 11, 2012
=
and cos(0) > 0, what is tan (0).
7°
(b)
q
(d)
9
4- Co 2
r
—
7-c-
Only one of the functions listed below is
6.
1
cos
(c)—
(o
J
z
3v)
(a)-
I
f(x)
(b) f(x)
cos (x)sin (x)
2 (x)cos (x)
sin
(c) f(x)=cos(x)
(d)f(x)=tan(x)cot(x)
(x)
2
(e) f(x) = tan
(a)
CJS 4
Which one is it?
—
(€iY(d)
=
=
j5?ë
(
—.
L
j
4t
—
0c&21
)L(
(o
You are standing 100 feet away from the base of a building. You see the very top when
7.
looking up at a 600 angle. What is the height of the building? (Assume your eye is at ground
level)
(a) 60 feet
(b) 100 feet
(c) 137 feet
I d
€i
(6O)
rZiZ3rS
(e) 196 feet
Let the point (2, —5) be on the terminal side of the angle 0. What is the value of
8.
sin (0)?
2
(a)
2
——
5
5
I
2
I
(b)—-
/‘
(e)
21
2I4
L
I
LI
—
29
N
1ø
1
sI
L
Summer 2012
June 11, 2012
Math 1060-003
Midterm #1
Which of the following is the reference angle of 0
9.
(a)
3
2rr
—
-
ZTr
(c)-
—
3
(d)
-:3?
(e)-
What is the period of the function y
10.
=
7 cos(5irx)
—
3
(a)-3
(b) 7
(c) 5ir
(d)
(e) 5
w
11.
5-
Which of the following functions has a maximum
(a) y=7sin(x)+1
(b) y = cos(7x)
—‘
—-
LcLiix)±7
1i)
x
vvoY
(
—
(d)y=3sin(x)+4
(e) y = sin (2x + 7)
7
rthY
12.
=
sin(2x)
(b) y
=
3cos (x)
(c) y
=
—sin(2irx)
(e) y
=
2sin (Trx) 1
I
VE(IVQ
Which of the following has a frequency off
(a) y
(I)
1
-
=
iJ
2-ii
(I)
c-rr
T1
Summer 2012
June 11, 2012
Math 1060-003
Midterm #1
Which function corresponds to the graph depicted here?
13.
(a) y
(b) y
(c) y
(d) y
(e) y
=
=
=
=
=
3sin (irx)
2cosC2irx)±1
2 sin(irx) + 1
—2 sin(2irx) + 1
—sin(irx)+ 1
3
L
1
uJ
1
fl
p%iZ
¶JL
2
-1
2
T
A bicycle wheel has a linear velocity of 20 meters per second and an angular velocity of
14.
5 radians per second. What is the radius of the wheel?
(b)
(c)
(d)
(e)
(f)
V
8
12
16
20
24
The earth rotates around the sun with a radius of approximately 90 million miles. In one
15.
month, the earth sweeps through an angle of approximately radians. Approximately how
many miles does the earth travel in one month?
(a)
(b)
(c)
(d)
(e)
lSir
3Oir
45ir
6Oir
907r
million
million
million
million
million
miles
miles
miles
miles
miles
rü
(5
S