Math 1060—003, Fall 2013
Instructor: Kyle Steffen
October 25, 2013
Name:
uNID:
Total points:
/55
Midterm Exam #2
INSTRUCTIONS: You have 50 minutes to complete this exam. No calculators, notes, books, neighbors,
etc. are allowed. To receive full credit, you must
• Clearly show your work,
• Use correct units (when applicable), and
• Place your final answer in the rectangle provided (when applicable).
You should simplify alifractions and expressions as much as possible, but you do not need to simplify
square roots or rationalize denominators.
points)
1. (2
Evaluate the following expressions.
(a) sin
(b) tan(—)
(,
4)
—)
tcAKU
-
If’(a)
(b)
points) Evaluate the following expressions.
(a) cos(_q)
--5
2. (2
(b) tan
1
(—;)
tomaiti
-7/
.-
4
Qcmaivi c
2.
coc’ 4-1
ckv1
“
‘I
I]
FR
—I
—
J-Uti
-SOf.9T[
+
(7C
TU
-‘
(a)
L
lnsuctor: Kyle Steffen
Math 1060—003
3. (4 points) Evaluate the following expressions.
(a) sin(arctan /)
(b) arccos(tan r)
()
Jj
Ccx’L
—3
(b)
+hc&-)
&ch
r4(Y1
2
..T1,
O11fL)
J)
1
s,(o 1-°
ih
-
aro(trru)
(a)
cir;c(o)
IC,
/2—
(b)
4. (4 points)
(a) Write down one of the co-function identities.
(b) Which trigonometric functions are even?
() cos(!!_-)zs;a.L
(‘ _{) ce’s
,
(a)
•csc(T --ta -
n(!L_é)cob(f)
c.iiØc)
(b)
Cb(-1).-Lan-L
5. (9 points) Two functions are given below. On the axes given, draw the asymptotes and the graph of
each function, using the entire length of the x-axis. For part (a), draw points (dots) on the graph where
f(x) = —1. For part (b), draw points (dots) on the graph where f(x) —2 and also where f(x) = 2.
-
A
EE
(a)f(x)=tanx—1
.E’f =
LiLi
-
‘
I
)__.___
E
=
-
(b)f(x)=—2secx
-
-
-
-
-
-
-
-
-
-
= = i::
-
-
-
-
-
-
j
-
-
-
==
-
Math O6O—OO3
Midterm Exam #1
lnstuctor: Kyle Steffen
6. (3 points) While waiting in line to ride the Merry-Go-Round at Lagoon, you estimate that the ride rotates
with an angular speed of 4 revolutions per minute. What is the angular speed of the ride in radians per
minute?
It is your turn to ride the Merry-Go-Round. If you want to go fast, should you take a seat which is close to
the center of the Merry-Go-Round, or a seat which is further away (closer to the edge)? (Hint: Consider
your linear speed. If it helps, suppose that the Merry-Go-Round has a radius of 20 feet.)
2TL
miyl
rads
4s
çjV
lTjVt
S
4
—
,d-ka
1
4 o’ a
lO-jer
Angular speed
Seat=
r
i-tJU4’
2r
=
rcLclS
mm
I
I
I
Fuvr
7. (6 points) Consider a right triangle with legs measuring 4 meters and 6 meters. What is the measure of
the smallest angle of the triangle? What is the measure of the length of the hypotenuse of the triangle?
Reminder: Show your work and use correct units. (Hint: The angle will be a trigonometric expression;
the hypotenuse will be an expression involving a square root.)
o rytt14
I
(s
Im
hyp-f
fl—Th
/12*
Smallest angle
52-
=
-L’( )
Length of hypotenuse
=
2 fi
CdJsS
€
4
Instructor: Kyle Steffen
Math 1060—003
points)
8. (3
The plots of three trigonometric functions are given below. The functions have
tions. Write the equation corresponding to each graph.
(a)
no transforma
(c)
(b)
4
U?
—2w
t
—It
/
\\\
-21
211
4\
(cl)y= Csc x
C(.o.c ?(
(b)y=
Sin
(A.kLfr1
(c)y=
points)
Circle each expression which, when simplified, is equal to 1. Show at least one step of your
9. (9
work in the space below each expression.
sin x tan x
2x
Sec
bu\
—
I
tan2x)
fcos
LJ)(
sec x
I
5oC
eZ
I
x
—r
sinx tanx secx
2 x + cos
‘sin
2x
?-flttiirti&s
+kvi.
tanxcotx
4o,ec)
S’x
.
Rc(c&Q i’thrh
taV\?(
10. (4
points) Expand and simplify (sinx + cosx)
.
2
(Sh IC)
..-
2
1 ?c)
(s
(S’x tco
(a,
L)
)
4
l3i?c CO/
I -i- 2 St,i
co 4
(sinx + cos x)
2
—
I
f-.S.,
L.k
1l
1xIkok.)
=
ft
Math 1060—003
Midterm Exam #1
Instructor: Kyle Steffen
5
11. (6 points) Verify the following identity
x—1
2
sec
.,
2
=sln x
sec- x
Clearly show your work. (Hint: Simplify the left-hand side. Compare the result with the right-hand side.)
2
Sc 2 )c— j
L.
/
- -sec
—.-
c—I)—-—
/
CbS(
I—CoSi(
b,
1
--c
)
12. (3 points) Factor the following expressions. Clearly show your work.
(a) sin
x—5sinxcosx
2
x—9
2
(b) tan
(tt)Sn.iyx
—six-(’.A)
_.corJ
()
(&b)(ft)
(a)
7
C
-
)
(t
(b)
-5c