Practice Test 3
Sections 5.5, 6.1, 6.2, 6.3, 6.4, and 6.5
Determine whether the given x-value is a solution of the
equation.
3π
1) cos 2x = - 2, x =
4
A) Yes
Use a calculator to solve the equation on the interval
[0, 2π). Round the answer to two decimal places.
13) tan x = 3.2
B) No
14) cos x = -0.83
2) cos x + 1 = sin x, x =
5π
4
A) Yes
Solve the triangle. Round lengths to the nearest tenth and
angle measures to the nearest degree. If there isn't a
triangle possible write not possible. If there are two
triangles possible, write the answers under the heading
triangle 1 and triangle 2.
15)
B) No
Find all solutions of the equation. Give answers in
radians.
3) sin x = 0
65°
4) 9 cos x + 6 2 = 7 cos x+ 5 2
9
Find all solutions of the equation.
5) tan x sec x = -2 tan x
45°
Solve the equation on the interval [0, 2π).
3
6) sin 4x =
2
7) cos 2x =
16)
2
2
7
6
8) 2 sin2 x = sin x
8
9) sin2 x - cos2 x = 0
17) A = 30°, a = 21, b = 42
10) sin2 x + sin x = 0
18) B = 50°
C = 104°
b = 19
11) -tan2 x sin x = -tan2 x
12) sin2 2x = 1
19) B = 104°, b = 5, a = 23
20) B = 17°, b = 13.8, a = 15.73
21) b = 2, c = 3, A = 85°
1
Find the area of the triangle having the given
measurements. Round to the nearest square unit.
22) A = 38°, b = 14 meters, c = 12 meters
30) 4,
-3π
4
5
23) a = 8 inches, b = 11 inches, c = 5 inches
24) C = 115°, a = 4 yards, b = 5 yards
-5
5
25) a = 22 yards, b = 12 yards, c = 13 yards
-5
Solve the problem.
26) To find the distance AB across a river, a
distance BC of 160 m is laid off on one side of
the river. It is found that B = 109.3° and
C = 15.8°. Find AB. Round to the nearest
meter.
31) -4,
5π
4
5
27) Two airplanes leave an airport at the same
time, one going N 35° W at 417 mph and the
other going due east at 329 mph. How far
apart are the planes after 4 hours (to the
nearest mile)?
-5
28) The distance from home plate to dead center
field in Sun Devil Stadium is 401 feet. A
baseball diamond is a square with a distance
from home plate to first base of 90 feet. How
far is it from first base to dead center field?
5
-5
32) (-4, -225°)
Use a polar coordinate system to plot the point with the
given polar coordinates.
9π
29) 2,
4
5
5
-5
-5
5
5
-5
-5
2
Find another representation, (r, θ), for the point under the
given conditions.
π
33) 7,
4
46) (x - 13)2 + y2 = 169
47) y2 = 3x
This is not multiple choice. Give an answer for
a - d.
Convert the polar equation to a rectangular equation.
48) r = 7
a) r > 0 and 2π < θ < 4π
b) r < 0 and 0 < θ < 2π
c) r > 0 and -2π < θ < 0
c) r < 0 and 2π < θ < 4π
49) θ =
5π
6
50) r = 5 csc θ
Select the representation that does not change the location
of the given point.
34) (8, 140°)
A) (-8, 500)°
B) (-8, 230)°
C) (8, 320)°
D) (8, 500)°
51) r cos θ = 9
52) r = 6 cos θ + 4 sin θ
Plot the complex number.
53) -4i
Polar coordinates of a point are given. Find the rectangular
coordinates of the point.
35) (-7, 120°)
36) 9,
i
6
4
3π
4
2
37) (4, -180°)
-6
-4
-2
2
4
6 R
2
4
6 R
-2
The rectangular coordinates of a point are given. Find
polar coordinates of the point. Express θ in radians.
38) (2, -2 3)
-4
-6
54) -3
39) (0, - 3)
i
6
40) (-5, 0)
4
41) (-4 2, -4 2)
2
-6
Convert the rectangular equation to a polar equation that
expresses r in terms of θ.
42) y = 9
-4
-2
-2
-4
-6
43) x2 + y2 = 25
44) x = 7
45) 8x - 7y + 10 = 0
3
55) -6 - i
61) -5i
i
6
Write the complex number in polar form. Express the
argument in radians.
62) - 2 3 - 2i
4
2
-6
-4
-2
2
4
63) 3 - 3i
6 R
-2
Write the complex number in rectangular form.
64) 9(cos 120° + i sin 120°)
-4
-6
65) -5(cos
56) 5 2 - 5 2i
3π
3π
)
+ i sin
4
4
i
66) 9(cos π + i sin π)
10
Find the product of the complex numbers. Leave answer in
polar form.
67) z 1 = 5(cos 35° + i sin 35°)
5
-10
-5
5
10
R
z 2 = 4(cos 8° + i sin 8°)
-5
68) z 1 = 8 cos
π
π
+ i sin
6
6
z 2 = 3 cos
π
π
+ i sin
2
2
-10
57) -4 +
3i
10
i
Find the quotient
z1
z2
of the complex numbers. Leave
answer in polar form.
69) z 1 = 14(cos 40° + i sin 40°)
5
z 2 = 2(cos 8° + i sin 8°)
-10
-5
5
R
-5
-10
70) z 1 =
3 cos
7π
7π
+ i sin
4
4
z2 =
6 cos
9π
9π
+ i sin
4
4
71) z 1 = 5(cos 200° + i sin 200°)
Find the absolute value of the complex number.
58) z = -3 + 6i
z 2 = 4(cos 50° + i sin 50°)
Use DeMoivre's Theorem to find the indicated power of
the complex number. Write the answer in rectangular
form.
72) 4(cos 15° + i sin 15°) 4
59) z = -15 + 4i
Write the complex number in polar form. Express the
argument in degrees.
60) -15 + 20i
4
73) 2 2 (cos
7π
7π 5
)
+ i sin
4
4
5
Answer Key
Testname: PRACTICE TEST 3
1) B
2) B
3) nπ
29)
5
4) x =
3π
5π
+ 2nπ or x =
+ 2nπ
4
4
5) x =
2π
4π
+ 2nπ or x =
+ 2nπ or x = nπ
3
3
6)
π π 2π 7π 7π 13π 5π 19π
, ,
,
,
,
,
,
12 6 3 12 6 12 3
12
7)
π 7π 9π 15π
,
,
,
8 8
8
8
8) 0, π,
9)
-5
π 5π
,
6 6
-5
π 3π 5π 7π
,
,
,
4 4
4 4
10) 0, π,
5
30)
5
3π
2
11) 0, π
π 3π 5π 7π
12) ,
,
,
4 4
4 4
13) 1.27, 4.41
14) 2.55, 3.73
15) B = 70°, a = 6.77, c = 8.68
16) A = 58°, B = 47°, C = 75°
17) B = 90°, C = 60°, c = 36.4
18) A = 26°, a = 10.9, c = 24.1
19) no triangle
20) A1 = 19°, C1 = 144°, c1 = 27.7;
-5
5
-5
31)
A2 = 161°, C2 = 2°, c2 = 1.6
21) a = 3.5, B = 35°, C = 60°
22) 52 square meters
23) 17 square inches
24) 9 square yards
25) 65 square yards
26) 53 meters
27) 2652 miles
28) 343.3 feet
5
-5
5
-5
6
Answer Key
Testname: PRACTICE TEST 3
32)
53)
i
5
6
4
2
-6
-5
-4
-2
5
2
4
6 R
2
4
6 R
2
4
6 R
-2
-4
-6
54)
-5
33) a) 7,
i
9
5
7
π b) -7, π c) 7, - π
4
4
4
d) -7,
6
4
13
π
4
2
34) D
7 -7 3
35) ,
2
2
36)
-6
-4
-2
-2
-9 2 9 2
,
2
2
-4
37) (-4, 0)
5π
38) 4,
3
-6
55)
i
6
39) (- 3, 90°)
40) (5, π)
41) (8, 225°)
9
42) r =
sin θ
4
2
43) r = 5
-6
44) r =
7
cos θ
45) r =
-10
(8 cos θ - 7 sin θ)
-4
-2
-2
-4
-6
46) r = 26 cos θ
47) r = 3 cot x cscx
48) x2 + y2 = 49
49) y = -
3
x
3
50) y = 5
51) x = 9
52) (x-3)2 + (y-2)2 = 13
7
Answer Key
Testname: PRACTICE TEST 3
56)
72) 128 + 128 3i
73) -128 + 128i
i
10
5
-10
-5
5
10
R
-5
-10
57)
10
i
5
-10
-5
5
R
-5
-10
58) 3 5
59) 241
60) 25(cos 126.9° + i sin 126.9°)
61) 5(cos 270° + i sin 270°)
7π
7π
62) 4 cos
+ i sin
6
6
63) 3 2 cos
64) 65)
7π
7π
+ i sin
4
4
9 9 3
i
+
2
2
5 2 -5 2
i
+
2
2
66) -9
67) 20(cos 43° + i sin 43°)
2π
2π
68) 24 cos
+ i sin
3
3
69) 7(cos 32° + i sin 32°)
2
3π
3π
70)
cos
+ i sin
2
2
2
71)
5
(cos 150° + i sin 150°)
4
8