Find the derivative of the function.
106)
y =x3 tan x
106)
A)
dy
dx =x3sec2x +3x2tan x
B)
dy
dx =x3 sec x tan x +3x2tan x
C)
dy
dx = – x3sec2 x +3x2tan x
D)
dy
dx =3x2sec2 x
If is an angle in the indicated quadrant, determine whether the given function is positive or negative.
107)
III, csc
107)
A)
Positive
B)
Negative
Find the derivative of the function.
108)
y = sin (ln 5x4)
108)
A)
dy
dx =4 cos (ln 5x4)
5x4
B)
dy
dx =4 cos (ln 5x4)
x
C)
dy
dx =
–4 cos (ln 5x4)
x
D)
dy
dx =5 cos (ln 5x4)
x
Give the exact value.
109)
cot 120°
109)
A)
–3
B)
–1
C)
–3
3
D)
3
3
Convert the degree measure to radians. Leave the answer as a multiple of .
110)
–650°
110)
A)
–65
36
B)
–65
9
C)
–29
18
D)
–65
18
If is an angle in the indicated quadrant, determine whether the given function is positive or negative.
111)
II, tan
111)
A)
Negative
B)
Positive
Find the integral.
112)
x2 sin 3x dx
112)
A)
– 3 x2 cos 3x + 18 x sin 3x + 54 cos 3x + C
B)
1
3x2 cos 3x –2
9x sin 3x –2
27 cos 3x + C
C)
–1
3x2 cos 3x +2
9x sin 3x +2
27 cos 3x + C
D)
–1
3x2 cos 3x +2
9x sin 3x + C
Solve the problem.
113)
The electric charge q, in Coulombs, passing a given point in a circuit is given by q = t csc (0.4t2+ 2),
where t is the time in seconds. Find the current i as a function of t (i = dq/dt).
113)
A)
dq
dt = csc (0.4t2+ 2) – 0.8t2 csc (0.4t2+ 2) cot (0.4t2+ 2)
B)
dq
dt = csc (0.4t2+ 2) –t csc (0.4t2+ 2) cot (0.4t2+ 2)
C)
dq
dt = csc (0.4t2+ 2) + 0.8t2 sec (0.4t2+ 2) cot (0.4t2+ 2)
D)
dq
dt = csc (0.4t2+ 2) – 0.8t2 csc (0.4t2+ 2) tan (0.4t2+ 2)
35
Evaluate the definite integral.
114)
/2
0
6 sin x dx
114)
A)
0
B)
–6
C)
1
D)
6
Find the exact value of the following expression without using a calculator.
115)
csc
3
115)
A)
2
B)
2 3
3
C)
2
D)
3
2
Use a calculator to find the function value to four decimal places.
116)
sin 0.2094
116)
A)
0.9782
B)
1.0223
C)
0.2125
D)
0.2079
Solve the problem.
117)
The voltage E in an electrical circuit is given by E =4.3 cos(80t), where t is time measured in
seconds. Find the period.
117)
A)
40
B)
40
C)
40
D)
1
40
Find all values of x between 0 and 2 that satisfy the equation.
118)
cos x = – 1
2
118)
A)
3,
3
B)
3,
3
C)
6, 11
6
D)
4,
4
Solve the problem.
119)
Snell’s Law states that c1
c2
=
sin 1
sin 2. Use this law to find the requested value. If c1=9×109,
c2=7.13 ×109,2=32°, find 1. Round your answer to the nearest degree.
119)
A)
1=42°
B)
1=43°
C)
1=40°
D)
1=45°
Find the derivative of the function.
120)
y =4
sin x +1
cot x
120)
A)
dy
dx = – 4 csc x cot x +sec2x
B)
dy
dx =4 cos x –csc2x
C)
dy
dx =4 csc x cot x –csc2x
D)
dy
dx =4 csc x cot x –sec2x
Solve the problem.
121)
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 April.
121)
A)
29,000
B)
29,965
C)
30,000
D)
29,500
Give the amplitude or period as requested.
122)
Period of f(x) =4cos(13x + 3)
122)
A)
4
B)
2
13
C)
2
13
D)
13
Give the exact value.
123)
csc 240°
123)
A)
–2 3
3
B)
–2
C)
2 3
3
D)
2
Solve the problem.
124)
The beacon on a lighthouse 50 m from a straight shoreline rotates twice per minute. Find dx/dt
where x is the distance along the shoreline from the point on the shoreline closest to the lighthouse
and the point where the beam hits the shoreline.
[Hint: Find an equation relating and x where is the angle between the beam of light and the line
from the lighthouse to the shoreline. Use the chain rule and express d/dt in radians per minute.]
124)
A)
dx
dt =200 sec tan
B)
dx
dt = – 200csc2
C)
dx
dt =200sec2
D)
dx
dt =50 sec2
Find the derivative of the function.
125)
y =sin 3x
cos 4x
125)
A)
dy
dx =3 cos 3x sin 4x +4 sin 3x cos 4x
cos24x
B)
dy
dx =3 cos 3x cos 4x –4 sin 3x sin 4x
cos24x
C)
dy
dx = cos 3x cos 4x + sin 3x sin 4x
cos24x
D)
dy
dx =3 cos 3x cos 4x +4 sin 3x sin 4x
cos24x
38
Solve the problem.
126)
The position of a weight attached to a spring is s(t) = – 7 cos(12t) inches after t seconds. What is
the maximum height that the weight reaches above the equilibrium position and when does it first
reach the maximum height?
126)
A)
The maximum height of 7 inches is first reached after 0.08 seconds.
B)
The maximum height of 14 inches is first reached after 3 seconds.
C)
The maximum height of 14 inches is first reached after 6 seconds.
D)
The maximum height of 7 inches is first reached after 6 seconds.
127)
At an altitude of 2700 ft, the engine on a small plane fails. What angle of glide is needed to reach an
airport runway that is 4 miles away by land? (Round your answer to the nearest tenth of a degree.)
127)
A)
8.3°
B)
88.9°
C)
89.9°
D)
7.3°
128)
The index of refraction for air, Ia, is 1.0003. The index of refraction for water, Iw, is 1.3. If
Iw
Ia
=sin A
sin W , and A = 31.5°, find W to the nearest tenth.
128)
A)
22.7°
B)
21.7°
C)
20.7°
D)
23.7°
If is an angle in the indicated quadrant, determine whether the given function is positive or negative.
129)
IV, cot
129)
A)
Negative
B)
Positive
Convert the degree measure to radians. Leave the answer as a multiple of .
130)
570°
130)
A)
19
3
B)
19
12
C)
19
5
D)
19
6
Find all values of x between 0 and 2 that satisfy the equation.
131)
sec x =2
131)
A)
6,
6
B)
6, 11
6
C)
4,
4
D)
3,
3
Use a calculator to find the function value to four decimal places.
132)
cos 46.5°
132)
A)
0.6884
B)
1.0538
C)
–0.8116
D)
0.7254
Convert the degree measure to radians. Leave the answer as a multiple of .
133)
620°
133)
A)
13
9
B)
31
18
C)
62
9
D)
31
9
Solve the problem.
134)
The temperature in Fairbanks is approximated by T(x) = 37 sin 2
365(x – 101) + 25, where T(x) is the
temperature on day x, with x = 1 corresponding to Jan 1 and x = 365 corresponding to Dec 31.
Estimate the temperature, to the nearest degree, on day 244.
134)
A)
48°
B)
23°
C)
292°
D)
–25°
Find the derivative of the function.
135)
y =sin x
4x +4x
sin x
135)
A)
dy
dx =x cos x – sin x
4x2+4 sin x –4x cos x
sin2x
B)
dy
dx =sin x – x cos x
16x2+4x cos x –4 sin x
sin2x
C)
dy
dx =x cos x + sin x
4x2+4 sin x +4x cos x
sin2x
D)
dy
dx =cos x
4+4
cos x
Find the indicated trigonometric function for , given that is an angle in standard position with the terminal side
defined by the given point.
136)
(3, 4); find csc
136)
A)
5
3
B)
4
3
C)
3
4
D)
5
4
D
Find the slope of the line tangent to the curve at the given point.
137)
y =15 sin x; x =
3
137)
A)
15
2
B)
–15
2
C)
15 3
2
D)
1
2
A
Find the derivative of the function.
138)
y = ln tan25x
138)
A)
dy
dx =10 sec 5x
B)
dy
dx =10 sec25x
tan 5x
C)
dy
dx = sec 5x csc 5x
D)
dy
dx =10
tan 5x
B
A
Find the integral.
139)
e5x csc e5x cot e5x dx
139)
A)
–1
5e5x csc e5x + C
B)
–1
5 csc e5x + C
C)
–1
5 cot e5x + C
D)
–1
5e5x cot e5x + C
If is an angle in the indicated quadrant, determine whether the given function is positive or negative.
140)
II, sin
140)
A)
Negative
B)
Positive
Answer Key
Testname: C13
Answer Key
Testname: C13
Answer Key
Testname: C13