Find the derivative of the function.
62)
y =5 sin (7x – 6)
62)
A)
dy
dx = – 7 cos (7x – 6)
B)
dy
dx =5 cos (7x – 6)
C)
dy
dx =35 cos (7x – 6)
D)
dy
dx =7 sin (7x – 6)
Convert the radian measure to degrees.
63)
–9
4
63)
A)
–202.5°
B)
–405°
C)
–212.5°
D)
–810°
Find the derivative of the function.
64)
y =cos x
x2
64)
A)
dy
dx =
–2 cos x – x sin x
x2
B)
dy
dx =
–2 cos x – x sin x
x3
C)
dy
dx =cos x – x sin x
x3
D)
dy
dx =2 cos x + x sin x
x3
Find the integral.
65)
4csc26x dx
65)
A)
–2
3 cot 6x + C
B)
2
3 cot 6x + C
C)
–2
3 tan 6x + C
D)
–24 cot 6x + C
Find the derivative of the function.
66)
y =(cos 2x + tan x5)4
66)
A)
dy
dx =4(– sin 2x +5x4 sec x5 tan x5)3
B)
dy
dx =4(cos 2x + tan x5)3(–2 sin 2x +5x4sec2(x5))
C)
dy
dx =4(cos 2x + tan x5)3(2 sin 2x +5x4cot2(x5))
D)
dy
dx =4(cos 2x + tan x5)3
Find the slope of the line tangent to the curve at the given point.
67)
y =6 cot x; x =
6
67)
A)
–24
B)
–6
C)
8
D)
24
A
Find the indicated trigonometric function for , given that is an angle in standard position with the terminal side
defined by the given point.
68)
(3, –4); find csc
68)
A)
4
5
B)
–5
3
C)
–5
4
D)
5
4
C
B
Solve the problem.
69)
A surveyor measures the distance between two markers to be 408 m. Then, moving along a line
equidistant from the markers, the distance d from the surveyor to each marker is d =204 csc 1
2,
where is the angle between the lines of sight to the markers. See the figure below. By using
differentials, find the change in d if changes from 94.7° to 94.95°
408 m
69)
A)
–0.5574 m
B)
0.03671 m
C)
–31.94 m
D)
–1.115 m
Give the exact value.
70)
sin 45°
70)
A)
2
B)
1
2
C)
3
2
D)
2
2
Give the amplitude or period as requested.
71)
Period of f(t) =5cos
9t + 3
71)
A)
9
B)
18
C)
18
D)
9
Find the indicated trigonometric function for , given that is an angle in standard position with the terminal side
defined by the given point.
72)
(–7, –2); find tan
72)
A)
7
2
B)
2
7
C)
– 1
D)
–2
7
Convert the degree measure to radians. Leave the answer as a multiple of .
73)
75°
73)
A)
4
11
B)
1
3
C)
5
12
D)
6
13
C
Solve the problem.
74)
The air speed of an airplane is 650 km/hr and its angle of climb is 4.60°. What is its ground speed
(to the nearest km/hr)?
74)
A)
648 km/hr
B)
638 km/hr
C)
643 km/hr
D)
633 km/hr
A
Find the integral.
75)
11x cos 1
2x dx
75)
A)
11x sin 1
2x– 22 cos 1
2x+ C
B)
11 sin 1
2x+ 22x cos 1
2x+ C
C)
44 sin 1
2x– 22x cos 1
2x+ C
D)
22x sin 1
2x+ 44 cos 1
2x+ C
D
Graph the function.
24
B
76)
y =2 cos x
76)
A)
B)
C)
D)
Use a calculator to find the function value to four decimal places.
77)
tan 695°
77)
A)
–1.4282
B)
0.0875
C)
0.9063
D)
–0.4663
Find the derivative of the function.
78)
y =10 + sec x
10 – sec x
78)
A)
dy
dx =20 tan2x
(10 – sec x)2
B)
dy
dx =20 sec x tan x
(10 – sec x)2
C)
dy
dx = – 2 sec2x tan x
(10 – sec x)2
D)
dy
dx = – 20 sec x tan x
(10 – sec x)2
Solve the problem.
79)
The velocity of a car is 82 sin t –60 kilometers per hour on the time interval [0, 2] hours. Assuming
that the odometer runs backward when the car has negative velocity, express the odometer reading
at the end of the time interval in terms of its reading at the beginning, R0.
79)
A)
–3.876 +R0
B)
164 +R0
C)
–5.039 +R0
D)
236.124 +R0
Convert the degree measure to radians. Leave the answer as a multiple of .
80)
60°
80)
A)
5
B)
4
C)
2
D)
3
Find the derivative of the function.
81)
y =3 sin 5x cos x
81)
A)
dy
dx = sin 5x sin x + 15 cos x cos 5x
B)
dy
dx = – 3 sin 5x sin x + cos x cos 5x
C)
dy
dx = – 3 sin 5x sin x + 15 cos x cos 5x
D)
dy
dx =3 sin 5x sin x + 15 cos x cos 5x
Find the exact value of the following expression without using a calculator.
82)
cos 5
6
82)
A)
–1
2
B)
–2
2
C)
–3
2
D)
3
2
Use a calculator to find the function value to four decimal places.
83)
tan 26.8°
83)
A)
1.9797
B)
–10.3346
C)
0.5051
D)
0.4509
Solve the problem.
84)
The velocity of a car is 63 cos t km/hr on the time interval [0, 2] hours. Calculate the distance the
car traveled in that time interval.
84)
A)
68.714 kilometers
B)
126 kilometers
C)
183.286 kilometers
D)
57.286 kilometers
27
Find the derivative of the function.
85)
y = cot (3x –4)
85)
A)
dy
dx =3 cot (3x –4) csc (3x –4)
B)
dy
dx = – 3 sec2(3x –4)
C)
dy
dx = – csc2(3x –4)
D)
dy
dx = – 3 csc2(3x –4)
Solve the problem.
86)
During a one–hour race, the velocities of two cars are v1(t) =59(1 – cos(t)) and v2(t) =113t, where
0 t 1. If, at the beginning of the race, both cars were at the mile 0 mark, which car won?
86)
A)
There is not enough information to determine the winner.
B)
Car 2
C)
Car 1
D)
It was a tie.
87)
The number of ducks (in thousands) counted at a certain checkpoint in their migration is given by
O(t) = 5 + 5 cos (t/6), where t is time in months and t = 0 is October. Find the number of ducks
passing the checkpoint between October and January.
87)
A)
24,549
B)
20,000
C)
17,618
D)
24,536
Find the integral.
88)
2x2 csc x3 cot x3 dx
88)
A)
6 csc x3+ C
B)
2
3 csc x3+ C
C)
–2
3x3 csc x3+ C
D)
–2
3 sec x3+ C
Find the exact value of the following expression without using a calculator.
89)
csc 5
3
89)
A)
–2
B)
–3
C)
–1
2
D)
–2 3
3
Find the derivative of the function.
90)
y =cos e–5x
90)
A)
dy
dx =5 sin e–5x
B)
dy
dx =e–5x cos e–5x
C)
dy
dx =5e–5xsin e–5x
D)
dy
dx = – 5e–5x sin e–5x
D)
91)
y = sec 3x
91)
A)
dy
dx =3 sec 3x tan 3x
B)
dy
dx =3 sec x tan x
C)
dy
dx =3 sec 3x cot 3x
D)
dy
dx = – sec 3x tan 3x
D)
Solve the problem.
92)
When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack’s line of
sight is 54°32‘. If Joey is known to be standing 23 feet from the base of the tree, how tall is the tree
(to the nearest foot)?
92)
A)
36 ft
B)
32 ft
C)
38 ft
D)
34 ft
D)
D)
Find the exact value of the following expression without using a calculator.
93)
sin
6
93)
A)
2
2
B)
1
2
C)
3
3
D)
3
2
Evaluate the definite integral.
94)
/2
0
cos2 x sin x dx
94)
A)
–3
B)
3
C)
1
3
D)
–1
3
Find the derivative of the function.
95)
y =tan x
2x –6
95)
A)
dy
dx =sec2x –2tan x
(2x –6)2
B)
dy
dx =(2x –6)sec2x –2tan x
(2x –6)2
C)
dy
dx =(2x –6)sec x tan x –2tan x
(2x –6)2
D)
dy
dx =(2x –6)csc2x –2tan x
(2x –6)2
If is an angle in the indicated quadrant, determine whether the given function is positive or negative.
96)
I, csc
96)
A)
Positive
B)
Negative
Graph the function.
30
97)
y =1
3 sin 3
4x
97)
A)
B)
C)
D)
Solve the problem.
98)
The number of ducks (in thousands) counted at a certain checkpoint in their migration is given by
O(t) = 5 + 5 cos (t/6), where t is time in months and t = 0 is October. Find the number of ducks
passing the checkpoint between October and November.
98)
A)
7500
B)
9775
C)
5796
D)
4775
Find the indicated trigonometric function for , given that is an angle in standard position with the terminal side
defined by the given point.
99)
(–10, –24); find cos
99)
A)
5
13
B)
–5
13
C)
–13
5
D)
–12
13
B
Solve the problem.
100)
A 34–foot ladder is leaning against the side of a building. If the ladder makes an angle of 28°35
with the side of the building, how far is the bottom of the ladder from the base of the building?
Round your answer to the hundredths place.
100)
A)
21.97 ft
B)
6.9 ft
C)
17.57 ft
D)
16.27 ft
D
Find all values of x between 0 and 2 that satisfy the equation.
101)
sin x =1
2
101)
A)
6, 11
6
B)
6,
6
C)
3,
3
D)
4,
4
B
B
Find the exact value of the following expression without using a calculator.
102)
sec 3
4
102)
A)
2
2
B)
–2
C)
–2
D)
–2 3
3
Give the amplitude or period as requested.
103)
Amplitude of f(x) = – 5 sin x
103)
A)
5
B)
2
C)
5
D)
–5
Find the derivative of the function.
104)
y = sin 2e5x
104)
A)
dy
dx = cos 2e5x
B)
dy
dx = – 10e5x cos 2e5x
C)
dy
dx =e5x cos 2e5x
D)
dy
dx =10e5x cos 2e5x
If is an angle in the indicated quadrant, determine whether the given function is positive or negative.
105)
III, cos
105)
A)
Positive
B)
Negative