102)
A department store has revenue from the sale of electrical kitchen appliances that is given
approximately by R(t) = 2.2 + 2.2 cos t
23 for 0 t 52, where R(t) is revenue in hundreds of dollars
for a week of sales t weeks after January 1. What is the total revenue (to the nearest hundred
dollars) earned from t = 10 to t = 16?
102)
A)
$300
B)
$1100
C)
$1300
D)
$1000
Find the indicated trigonometric function, where is the radian measure of the given angle. Give an exact answer with a
rational denominator.
103)
Find sin .
5
8
103)
A)
89
8
B)
589
89
C)
889
89
D)
89
5
Find the slope of the line tangent to the curve at the given point.
104)
y =25 cos x; x =
4
104)
A)
25 3
2
B)
–25
2
C)
25 2
2
D)
–25 2
2
Differentiate.
105)
f(x) =(sin x + cos x)5
105)
A)
5(sin x + cos x)5
B)
5(sin x + cos x)4(cos x – sin x)
C)
5(sin x + cos x)4
D)
(cos x – sin x)5
E)
none of these
E)
Convert the angle from degrees to radians. Express the answer as a multiple of .
106)
–60°
106)
A)
–
2
B)
–
3
C)
–
5
D)
–
4
B
B)
107)
Give the value of sin t where t is the radian measure of the angle shown.
107)
A)
2
B)
2
8
=2
2
C)
–2
2= – 1
D)
–2
E)
none of these
B
B)
E)
B
B)
Find the derivative of the function.
108)
y =cos e2x
108)
A)
dy
dx = – 2 sin e2x
B)
dy
dx =2e2x sin e2x
C)
dy
dx = – 2e2xsin e2x
D)
dy
dx =e2x cos e2x
109)
y =4 sin 4x cos x
109)
A)
dy
dx = – 4 sin 4x sin x + cos x cos 4x
B)
dy
dx = sin 4x sin x + 16 cos x cos 4x
C)
dy
dx =4 sin 4x sin x + 16 cos x cos 4x
D)
dy
dx = – 4 sin 4x sin x + 16 cos x cos 4x
110)
Find the t such that 0 t and cos t = cos –
3.
110)
A)
6
B)
2
3
C)
–
3
D)
3
E)
none of these
111)
Find the tangent line to the graph of f(x) = sin x + cos x at (, –1).
111)
A)
y =
B)
y = x +
C)
y = – x + –1
D)
y = – x + 1
E)
none of these
Use the properties of the sine and cosine to solve the problem.
112)
Assume cos(0.67) =0.78
Find sin(0.67), cos(–0.67), and cos(0.67 –2).
112)
A)
sin(0.67) =0.22
cos(–0.67) = – 0.78
cos(0.67 –2) = – 0.78
B)
sin(0.67) =0.63
cos(–0.67) =0.78
cos(0.67 –2) =0.78
C)
sin(0.67) =0.63
cos(–0.67) = – 0.78
cos(0.67 –2) = – 0.78
D)
sin(0.67) = – 0.63
cos(–0.67) =0.22
cos(0.67 –2) =0.78
Find the slope of the line tangent to the curve at the given point.
113)
y =25 sin x; x =
2
113)
A)
25
B)
0
C)
25
2
D)
–25
Find the indefinite integral.
114)
3 sin(t –) dt
114)
A)
–3 cos(t –) + C
B)
3 cos(t –) + C
C)
–3 cos t + C
D)
3 cos(t –) + C
E)
none of these
Find the indicated trigonometric function, where is the radian measure of the given angle. Give an exact answer with a
rational denominator.
115)
Find cos .
8
9
115)
A)
145
9
B)
145
8
C)
9145
145
D)
8145
145
Differentiate.
116)
(sin 3t)2
116)
A)
2 sin 3t
B)
6 sin 3t
C)
6 sin 3t cos 3t
D)
2 sin 3t cos 3t
E)
none of these
Find the derivative of the function.
117)
y = cot (3x –6)
117)
A)
dy
dx = – csc2(3x –6)
B)
dy
dx = – 3 sec2(3x –6)
C)
dy
dx = – 3 csc2(3x –6)
D)
dy
dx =3 cot (3x –6) csc (3x –6)
Differentiate.
118)
sin x
x
118)
A)
cos x
x
B)
cos x
C)
1
xcos x –1
x2sin x
D)
none of these
Find the derivative of the function.
119)
y =x7– csc x +4
119)
A)
dy
dx =x6–cot2x +4
B)
dy
dx =7x6+ csc x cot x
C)
dy
dx =7x6– csc x cot x
D)
dy
dx =7x6+cot2x
Convert the angle from degrees to radians. Express the answer as a multiple of .
120)
30°
120)
A)
5
B)
7
C)
6
D)
8
Solve the problem.
121)
The velocity of a car is 61 cos t km/hr on the time interval [0, 2] hours. Calculate the distance the
car traveled in that time interval.
121)
A)
122 kilometers
B)
177.467 kilometers
C)
55.467 kilometers
D)
66.533 kilometers
122)
Convert –150° to radian measure.
122)
A)
7
6
B)
–5
6
C)
–5
3
D)
5
3
E)
none of these
Integrate.
123)
1
0
sec2x
4 dx
123)
A)
4
B)
2
C)
–
4
D)
4
E)
none of these
Differentiate.
124)
sin x5
124)
A)
5x4 cos x5
B)
5(sin x)4 cos x
C)
5 sin x4
D)
5x cos x5
125)
Find the tangent line to the graph of f(x) =(1 + sin x)3 at
2, 8 .
125)
A)
y =
2x – 8
B)
y = x – 8
C)
y = – 8
D)
y = 8
E)
none of these
Find the derivative of the function.
126)
y = cos x4
126)
A)
dy
dx =4 sin x4
B)
dy
dx = – 4x3 sin x4
C)
dy
dx = sin x4
D)
dy
dx = – 4x4 sin x4
127)
Convert 327° to radian measure.
127)
A)
109
120
B)
109
60
C)
109
120
D)
109
60
Find the derivative of the function.
128)
y = cos (4x2+ 5)
128)
A)
dy
dx =8x sin (4x2+ 5)
B)
dy
dx = sin (4x2+ 5)
C)
dy
dx = – 8 sin 4x2
D)
dy
dx = – 8x sin (4x2+ 5)
Convert the angle from degrees to radians. Express the answer as a multiple of .
129)
–810°
129)
A)
–9
B)
–9
4
C)
9
2
D)
–9
2
Find the slope of the line tangent to the curve at the given point.
130)
y =17 sin x; x =
3
130)
A)
–17
2
B)
17 3
2
C)
1
2
D)
17
2
Differentiate.
131)
ex3sin x3
131)
A)
3x2ex3(sin x3+ cos x3)
B)
ex3(sin x3+ cos x3)
C)
3x(ex3+ cos x3)
D)
3x2(ex3+ cos x3)
Find the derivative of the function.
132)
y =6 sin x3
132)
A)
dy
dx =18x2 cos x2
B)
dy
dx =18x3 cos x3
C)
dy
dx = x cos x3
D)
dy
dx =18x2 cos x3
133)
y =3 sin (7x – 3)
133)
A)
dy
dx =7 sin (7x – 3)
B)
dy
dx =3 cos (7x – 3)
C)
dy
dx =21 cos (7x – 3)
D)
dy
dx = – 7 cos (7x – 3)
134)
Find t such that –
2 t
2 and sin t = sin
4.
134)
A)
–
3
B)
2
C)
4
D)
6
E)
none of these
135)
Find t such that 0 t
2 and sin t = cos t.
135)
A)
3
B)
4
C)
8
D)
0
E)
none of these
136)
Find the area under the curve y = sin 2x from x = 0 to x =
4.
136)
A)
1
2
B)
4
3
C)
0
D)
–1
E)
none of these
A
B
Use the properties of the sine and cosine to solve the problem.
137)
Assume sin(0.56) =0.53
Find cos(0.56), sin(–0.56), and cos
2–0.56 .
137)
A)
cos(0.56) = – 0.85
sin(–0.56) =0.53
cos
2–0.56 =0.53
B)
cos(0.56) =0.85
sin(–0.56) = – 0.53
cos
2–0.56 =0.53
C)
cos(0.56) =0.85
sin(–0.56) =0.53
cos
2–0.56 = – 0.53
D)
cos(0.56) =0.47
sin(–0.56) = – 0.53
cos
2–0.56 =0.85
Differentiate.
138)
cos 2t cos 3t
138)
A)
–2sin 2t cos 3t – 3cos 2t sin 3t
B)
2sin 2t cos 3t + 3cos 2t sin 3t
C)
–sin 2t cos 3t – cos 2t sin 3t
D)
none of these
Find the indicated trigonometric function, where is the radian measure of the given angle. Give an exact answer with a
rational denominator.
139)
Find tan .
3
5
139)
A)
34
5
B)
3
5
C)
34
3
D)
5
3