Name:
Math 1060—003, Fall 2013
Instructor: Kyle Steffen
November 22, 2013
I YWf
uNID:
Midterm Exam #3
INSTRUCTIONS: You have 50 minutes to complete this exam. No notes, books, neighbors, etc. are
allowed.
• Show your work!
•
•
•
•
•
•
•
Box your answer.
Scieiitf-ic calculators are allowed on #7—9. Other questions must be answered without a calculator.
Show what you put into the calculator!
Round (nearest 0.01) and include units.
Draw a picture if necessary.
Simplify answers.
The exam is worth 100 points. Each page is worth 25 points.
Page 1
Page 2
Page 3
Page 4
Total
Useful formulas:
sin(u+v)
=
sinucosv +cosusinv
cos(u + v)
=
cosucosv
tan(u+v)=
tanu+Oflv
1—tanutanu
—
b
a
=
c
+
2
—
2abcosC
AT=absinC
sinusinv
sin
=
cos
=
sinu
—---=-----
sinA
sinB
AT=Js(s—a)(s—b)(s—c)
Math 060 003
1. Find the exact value of sec( +
Instructor: Kyle Strum
given the triangle below.
n/
)
4
,
COS(i
I)
4
-
lb
lb
-.
--i
-
j4--34:.
‘
2.
l0
--
H
2. Consider two angles: A = 225°, B
(a) sin(A B)
(b) tan(A/2)
=
150°. Find the exact value of
—
o(22) S’i(1°)
zs;I1(220) o(Lso0)
- —4_i
-
-
-
-;
-.
z
-
1— C3225°
-,
;--
(a)
2
l—-i-J
2-
—
J
(b)
3. Verify the following idñity
csc
x
2
—1
2x
csc
_i
=cos 2 x
*_.
:::
SI(Y
43 lr
-
-=
A
2
n
1
S
I
m.5CrA
x
—
Math 1060—00:3
Mitherm Exam 11:3
Instructor: Kyle Steffen
3
4. Solve for all values of x. Your answer should be exact (i.e. do not use a calculator). Hint: Your answer for
this problem should include “n”.
4cos(5x) —2
0
=
-z
cs(x) ‘f
Jcos
Ov
(5t)
-the .&vif CI(CCL
,
7C
I” r0,2?)
‘57c
-rt
4 21C Vi
21C
-
it
2-rc &
4
15
—
4.
5. Solve for all values of x in the interval [0, 2it). Your answer should be exact.
2 x + sinx
sin
%I(lX2
=
2
0
o
-Sivics2O
I
VT
•
/
VL
4
Instructor: Kyle Stellen
Math 1060—003
6. Solve for all values of x in the interval [0, 2n). Your answer should be exact.
sin
x
—
2
—
c
cos x =0
dr.Q
(S
0
S‘
r
S
‘
2-
Sru
S QZLG
-
(f
c o.s
—Mx
(OX
(sx
- ‘
—f
Xc
I
-
)
—
-
4—
6.
I_______________
-it
7. Consider a triangle ABC with a = 18 ft, A = 25’, and B = 72g. Draw a figure, show your work, and use
your calculator to answer the following questions.
(ci) Solve for the unknown measurements (b, c, and C). Note: There is one and only one triangle for the
given data a,A,B.
(b) Compute the area of the triangle.
c_
lst
CL
&
C
C--
Sv1C-•
i83
.3’
2
1O.5I &
(a)
{
4
Q4227
(b)
z
11
—
A
.
i’
(..c
r
.
Tt
<os
Ii
*
OL’
V (-I) i
-
O
Math 1O6OOO:l
Mdterrn Kxani /3
lnIrLlcEor: Kyle Steflen
5
8. A pilot flies due North for 150 miles, then turns left 70° and continues flying for 200 miles. Draw a figure,
show your work, and use your calculator to answer the following questions.
(a) How far is the pilot from her starting point?
(b) What is the bearing from start to finish?
i-2-oc
j5O
,2-5Oo
C-
C
scvi
9
Z22 .13
lob’
t
sO
&
WOr1i
—
200
-.
I,O
o
0
c
.s(Ia0)
rv
(a)
C
(b)N
0
4
.tI
N
9. Distance from shore: At a point A you observe that the angle between the shore and the center of an island
is 30°. At a point B, which is 50 meters away from point A, you observe that the angle is now 40°. How
far is the island from shore? (See the figure for more information.)
TSIcrft(
c_
cL
v4-.!xt%r
s-k-n
vo1.
vfio.
4
.
--
A
0
50
a-
vYL
9.
—
—,
17.