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HOMEWORK4
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Express the product as a sum or difference.
1) sin 5x cos 2x
1
A) (sin 7x + sin 3x)
2
C)
1)
B) sin (cos 10x2 )
1
(sin 7x + cos 3x)
2
D)
1
(cos 7x - cos 3x)
2
Solve the problem.
2) sin 10x + sin 4x
A) 2 cos 7x sin 3x
2)
B) 2 sin 7x sin 3x
C) 2 sin 7x cos 3x
D) 2 sin 14x
Express the product as a sum or difference.
3) sin 3x cos 4x
1
A) (sin 7x - sin x)
2
C)
3)
B) sin (cos 12x2 )
1
(cos 7x - cos x)
2
D)
1
(cos 7x + sin x)
2
Solve the problem.
4) cos 8x - cos 4x
A) 2 cos 2x
4)
B) -2 sin 6x sin 2x
C) 2 cos 6x cos 2x
D) -2 cos 6x sin 2x
Express the product as a sum or difference.
5) cos 2x cos 4x
1
A) (cos 6x - sin 2x)
2
C)
5)
B) cos2 6x2
1
(cos 6x - cos 2x)
2
D)
1
(cos 2x + cos 6x)
2
Solve the problem.
6) cos 3x - cos 5x
A) -2 cos 4x sin x
6)
B) cos (-2x)
C) -2 sin 4x sin x
Use substitution to determine whether the given x-value is a solution of the equation.
3
4
, x=
7) sin x = 2
3
A) Yes
B) No
1
D) 2 sin 4x sin x
7)
8) cos x + 1 = sin x, x =
5
4
8)
A) Yes
B) No
Solve the equation on the interval [0, 2 ).
3
9) cos 2x =
2
A)
C)
12
,
9)
11 13 23
,
,
12 12 12
B)
3
2
D)
10) cos2 x + 2 cos x + 1 = 0
7
A) ,
4 4
11) 2 sin2 x = sin x
2
A) ,
3 3
B) 2
6
,
11
6
2
3
D) ,
2 2
C)
B) 0, ,
6
,
5
6
C)
6
,
5
6
D)
2
,
3
2
, ,
2 3 3
12) sec2 x - 2 = tan2 x
A)
11)
12)
B) no solution
6
10)
C)
D)
4
3
Solve the equation on the interval [0, 2 ).
13) tan2 x sin x = tan2 x
A)
2
, ,2
13)
B)
2
,
C) 0,
D) 0,
2
2
,
Solve the equation on the interval [0, 2 ).
x
x
14) sec = cos
2
2
A)
C)
14)
2 7 7 13 5
, ,
,
,
,
,
12 6 3 12 6 12 3
4
,
B) 0,
5
4
4
, ,
5
3
D) 0
Use a calculator to solve the equation on the interval [0, 2 ). Round the answer to two decimal places.
15) sin x = 0.38
A) 0.39, 2.75
15)
B) 0.39, 1.96
C) 0.39, 5.89
D) 0.39, 3.53
16) cos x = 0.60
A) 0.93, 2.21
16)
B) 0.93, 5.36
C) 0.93, 2.50
2
D) 0.93, 4.07
Solve the problem.
17) The output voltage for an AC generator is approximated by v = 156 cos (120 t -
3
). Find the
17)
smallest positive value of t for which the output is 49 volts.
A) 0.0132 second
B) 0.0051 second
C) 0.0061 second
D) 0.0122 second
Solve the triangle.
18)
18)
75°
7
50°
A) B = 60°, a = 6.55, c = 8.25
B) B = 55°, a = 8.25, c = 6.55
C) B = 55°, a = 6.55, c = 8.25
D) B = 50°, a = 8.25, c = 6.55
Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle,
two triangles, or no triangle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measures
to the nearest degree.
19) A = 30°, a = 22, b = 44
19)
A) B = 60°, C = 90°, c = 38.1
B) B = 60°, C = 60°, c = 38.1
C) B = 90°, C = 60°, c = 38.1
D) no triangle
Find the area of the triangle having the given measurements. Round to the nearest square unit.
20) A = 30°, b = 15 inches, c = 5 inches
20)
A) 19 square inches
B) 32 square inches
C) 34 square inches
D) 17 square inches
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.
21)
21)
9
6
4
A) A = 127.2°, B = 32.1°, C = 20.7°
B) A = 32.1°, B = 20.7°, C = 127.2°
C) A = 32.1°, B = 127.2°, C = 20.7°
D) A = 127.2°, B = 20.7°, C = 32.1°
3