Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1)
Which of the following statements is false?
1)
A)
The degree measure of = – 5
4 is 135°.
B)
The terminal side of the angle =13
6 lies in the first quadrant.
C)
The terminal side of the angle = – 3
4 lies in the fourth quadrant.
D)
The degree measure of =13
6 is 390°.
2)
Suppose
4 x 3
4. Which of the following statements can be made about tan x?
2)
A)
tan x is not defined.
B)
tan x is defined.
C)
If tan x is defined, then |tan x| 1.
D)
tan x is positive.
E)
none of these
3)
Find the equation of the line tangent to the graph of y = sin 2x at x =
2?
3)
A)
y – 1 = x –
2
B)
y = (cos 2x) x –
2
C)
y = – x –
2
D)
y = – 2x –
E)
none of these
4)
Find the tangent line to the graph of f(x) =cos22x at
2, 1 .
4)
A)
1
B)
–1
C)
2
D)
–2
E)
none of these
E
E
5)
Which of the following angles could represent the angle –17
12 ?
5)
A)
B)
C)
D)
none of these
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the indefinite integral.
6)
sin(3t + 2)dt
Enter your answer using parentheses around the argument of the function.
6)
Differentiate.
7)
esin(cos t)
Enter cosine before sine (except in the given exponential) and use parentheses around
arguments.
7)
8)
x sin x
8)
Find the indefinite integral.
9)
4 sin 2t dt
Enter your answer without parentheses.
9)
10)
Give the values of sin t and cos t, where t is the radian measure of the angle shown.
Enter your answer as a, b (unlabeled) where a represents sin t and b represents cos t.
10)
11)
Find the area under the curve y = sin(3t –) for
3 t 2
3.
Enter just a reduced fraction.
11)
Differentiate.
12)
f(t) = cot 1
t
Enter just an unlabeled quotient of functions of t. No parentheses.
12)
13)
Find the slope of the tangent line to the graph of y =e3x cos x3 at the origin.
Enter just an integer.
13)
Differentiate.
14)
f(x) =ex3· tan 2x
Enter your answer without parentheses except as indicated in this form, eP(x)(ab + 2d).
14)
Convert the given angle to degree measure.
15)
3
15)
Differentiate.
16)
cos2 x sin3 x
Enter cosine before sine in all terms, no parentheses around the arguments.
16)
Convert the given angle to degree measure.
17)
–
15
17)
Differentiate.
18)
2 cos2(4t)
Enter cosine terms before sine terms, no parentheses around arguments.
18)
19)
Give the values of tan t and sec t where t is the radian measure of the angle shown.
Enter just a, b where a represents tan t and b represents sec t, fractions and quotients
reduced of form c
d or f
g (no labels and no approximations).
19)
Integrate.
20)
sec2 5x dx
Enter your answer without parentheses.
20)
5
21)
Refer to the triangle whose sides and angles are labeled below. Estimate t if a = 24, b = 10,
and c = 26.
Enter just a real number rounded to one decimal place.
21)
Differentiate.
22)
f(x) =csc3x
Enter your answer without parentheses, no labels, use the multiplication dot between
functions of x.
22)
23)
cos(cos x)
Enter sines before cosines with parentheses around arguments and a multiplication dot
between the first two terms.
23)
Convert the given angle measure to radians. Give an exact answer.
24)
–210°
24)
25)
Find t such that 0 t and cos t = cos –7
6.
Enter just a reduced quotient of form a
b with in the numerator (unlabeled).
25)
Differentiate.
26)
sin x2
Do not enter parentheses around arguments.
26)
27)
f(x) =tan x + sin x
Enter your answer without parentheses, no labels. Enter a quotient a
b c .
27)
28)
Find the slope of the line tangent to the graph of y =cos2 4t at t =
3.
Enter just a b.
28)
Integrate.
29)
/4
0
sec2 x dx
Enter just an integer.
29)
30)
Refer to the triangle whose sides and angles are labeled below. If t = 0.6 and a = 4.1, find b.
Enter just a real number rounded to one decimal place (unlabeled).
30)
31)
Determine the value of sin t and cos t when t = 3.
Enter your answer as just a, b where a represents sin t and b represents cos t (no labels)
31)
Convert the given angle to degree measure.
32)
29
6
32)
Find the indefinite integral.
33)
cos 7x dx
Enter your answer without parentheses.
33)
34)
A person’s blood pressure P at time t is given by P(t) = 90 + 30 sin 7t
3, where t is
measured in seconds. What is the average blood pressure over a time interval of 60
seconds?
Enter just an integer (no units).
34)
Differentiate.
35)
ln(sin 3t)
Enter a quotient in terms of cosine and sine, no parentheses around arguments.
35)
36)
f(t) =(sec 3 t)6
Enter your answer without parentheses or labels, use a multiplication dot between the last
two functions.
36)
37)
Find the equation of the tangent line to the graph of y = ln(tan x) at x =
4.
Enter your answer in standard slope–intercept form with any quotients reduced with in
the numerator.
37)
Differentiate.
38)
sin x cos 3x
Enter cosine terms first, no parentheses around arguments.
38)
39)
f(x) = 2 sec x
Enter your answer without parentheses, secants before tangents in terms, no labels.
39)
40)
A ladder leaning against a building makes an angle of 60° with the ground. If the base of
the ladder is 3 feet from the building, how far up the building will the ladder reach? Enter
your answer in the reduced form a b (no units).
40)
Convert the given angle measure to radians. Give an exact answer.
41)
–55°
41)
Differentiate.
42)
cos2(x + 4)
Enter cosines before sines with parentheses around arguments.
42)
–2 cos(x + 4) sin(x + 4)
43)
cos x
sin x – 2
Enter a quotient of sine functions without parentheses around the arguments of sine.
43)
44)
f(x) = sec x
Enter your answer without parentheses, no labels, leave x in your answer which should
be entered as a quotient ab
c in terms of functions of x.
44)
Convert the given angle measure to radians. Give an exact answer.
45)
15°
45)
46)
780°
46)
9
47)
6°
47)
48)
10°
48)
Find the indefinite integral.
49)
sin t cos t dt
Enter your answer in terms of cosine without using parentheses.
49)
Differentiate.
50)
sin3(x3)
Enter sine terms before cosine terms with parentheses around arguments.
50)
Convert the given angle measure to radians. Give an exact answer.
51)
760°
51)
Differentiate.
52)
sin3(3t)
Enter sines before cosines with parentheses around arguments.
52)
Convert the given angle to degree measure.
53)
–
53)
54)
Find the slope of the line tangent to the graph of y = sin 2t at t =
3.
Enter just an integer.
54)
Differentiate.
55)
f(t) = ln(sec t)
Do not label your answer, no parentheses.
55)
56)
Give the values of sin t and cos t, where t is the radian measure of the angle shown.
Enter your answer as a, b (unlabeled) where a represents sin t and b represents cos t.
56)
Differentiate.
57)
f(x) = sec x2
Enter your answer without parentheses or labels. Use the multiplication dot between the
last two functions of x.
57)
58)
sin 3x
No parentheses around arguments.
58)
59)
3 cos x sin 2x
Enter cosine terms first, no parentheses around arguments.
59)
60)
Evaluate:
/2
0
sin x dx
Enter just an integer.
60)
Integrate.
61)
/2
0
sec2x +
4 dx
Enter just an integer.
61)
Differentiate.
62)
f(x) = ln(ex· tan 2x)
Enter your answer without parentheses or labels, no multiplication dot.
62)
63)
f(t) = csc t–3
Enter your answer without parentheses or labels. No multiplication dots. Enter your
answer as a quotient leaving t–3 in that form.
63)
64)
Does this represent an angle of –3
4 radians?
Enter “yes” or “no”.
64)
Differentiate.
65)
f(x) = 2 cot3 x
Enter your answer without parentheses, no labels, use the multiplication dot between
functions..
65)
Find the indefinite integral.
66)
cos 2t dt
Enter your answer without parentheses.
66)
67)
A river is 600 m wide. A boat enters the water and is pushed by the current at an angle of
30° to its original position. How far downstream from its original position will the boat
land?
Enter your answer in the reduced form a b (no units).
67)
Find the indefinite integral.
68)
3 cos(2x)dx
Enter your answer using parentheses around the argument of the function.
68)
Differentiate.
69)
6x cos2(sin x)
Enter cosines before sines in terms using parentheses around arguments.
69)
Find the indefinite integral.
70)
sin 4t dt
Enter your answer without parentheses around the argument of the function.
70)
Differentiate.
71)
ex3 sin x3
Enter your answer in the form P(x)eQ(x)·(sinR(x) ± cosS(x)) where P, Q, R, S are
polynomials in x in standard form. No parentheses around the arguments of sine and
cosine.
71)
Convert the given angle to degree measure.
72)
2
72)
73)
Give the values of tan t and sec t, where t is the radian measure of the angle shown.
Enter just a, b where a represents tan t and b represents sec t with any fractions reduced of
form c
d (no labels and no approximations).
73)
Differentiate.
74)
ln(1 + sin x)
Enter a quotient of sine and cosine functions without parentheses around their arguments.
74)
75)
f(t) =sec 3t
tan 5t
Enter your answer without parentheses or labels. Enter a quotient of functions of t of form
a–b
c using multiplication dots between all functions of t.
75)
76)
f(x) = tan(3x) sin x
Enter your answer without parentheses, no labels, any term containing sine appearing first.
76)
77)
Refer to the triangle whose sides and angles are labeled below. If t = 0.5 and a = 5, find c.
Enter just a real number rounded to one decimal place (unlabeled).
77)
78)
Find t such that –
2 t
2 and sin t = sin 10
3.
Enter just a reduced quotient of form a
b with in the numerator (unlabeled).
78)
Integrate.
79)
csc2(3x + 1) dx
Enter your answer using parentheses around the argument of the function.
79)
Differentiate.
80)
f(x) = ln(tan x) + tan x
Enter your answer exactly in the form a · (b + c).
80)
81)
Find the slope of the tangent line to the graph of y =etan x at x = 0.
Enter just an integer.
81)
82)
Suppose in a study of a prarie dog town it is discovered that the number of prarie dogs at
any time t is given by P(t) = 1000 + 500 cos 2t
12 , where t is measured in months from July
1, 1990. What is the average number of prarie dogs living in the town from July 1, 1990 to
July 1, 1992?
Enter just an integer.
82)
Convert the given angle to degree measure.
83)
5
83)
84)
Find t such that 0 t and cos t = cos –2
3.
Enter just a reduced quotient of form a
b with in the numerator (unlabeled).
84)
Differentiate.
85)
f(t) = tan t6
Enter your answer without parentheses, no labels.
85)
86)
f(x) =sin x2
tan x
Enter a quotient with cosine and sine functions last in their terms. No parentheses or labels
or multiplication dots.
86)
87)
Give the values of tan t and sec t, where t is the radian measure of the angle shown.
Enter just a, b where a represents tan t and b represents sec t. (no labels and no
approximations).
87)
88)
The size of an animal population at time t is given by N(t) = 50,000 + 200 sin 7t
48 , where t
is the number of months from June 1, 1980. At what rate is the animal population
changing on June 1, 1981?
Enter your answer as a quotient reduced form a
b with in the numerator (no units).
88)
Integrate.
89)
5
cos2 3x dx
Enter your answer without parentheses.
89)
90)
The U.S. Geological Survey estimates that the normal stream flow of the Potomac River (in
millions of gallons per day) is given by the function f(t) = 4200 + 3000 cos
6t +5
12 where t
denotes the number of months after January 1. Determine the maximum and minimum
daily stream flows of the Potomac River. Enter your answer exactly as a, b where a
represents the maximum and b represents the minimum,both integers separated by a
comma, no units or words.
90)
91)
Find the equation of the tangent line tangent to the graph of y = cos 3x + 2 sin x at x =
2.
Enter your answer in standard point–slope form.
91)
Differentiate.
92)
sin 3x2
Do not enter parentheses around arguments.
92)
93)
Find the area under the curve y = sin 2x + cos x for 0 x
4.
Enter as a+ b
2.
93)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the indicated trigonometric function, where is the radian measure of the given angle. Give an exact answer with a
rational denominator.
94)
Find sin .
7
4
94)
A)
433
33
B)
33
7
C)
4
7
D)
733
33
Convert the angle from degrees to radians. Express the answer as a multiple of .
95)
–430°
95)
A)
–43
9
B)
–43
36
C)
–7
18
D)
–43
18
96)
Determine the value of cos t when t = – .
96)
A)
1
B)
2
2
C)
–1
D)
–2
E)
none of these
Differentiate.
97)
sin x
cos x
97)
A)
1
B)
1
cos2x
C)
sin2x
cos2x
D)
–cos x
sin x
B
Find the indefinite integral.
98)
cos(2x + 1) dx
98)
A)
1
2sin(2x + 1) + C
B)
2cos (2x + 1) + C
C)
–cos (2x + 1) + C
D)
sin (2x + 1) + C
E)
none of these
A
C
Differentiate.
99)
f(x) = tan(cos x)
99)
A)
tan(–sin x)
B)
sec2(cos x)
C)
–sin x sec2(cos x)
D)
tan(cos x) sec(cos x)
E)
none of these
100)
Suppose sin t = – 5
13 and cos t is negative. What is cos t?
100)
A)
–12
13
B)
–18
13
C)
11
13
D)
–8
13
E)
none of these
Explanation:
Convert the angle from degrees to radians. Express the answer as a multiple of .
101)
360°
101)
A)
2
B)
5
2
C)
4
D)
3
2
Explanation:
Explanation: