Download Math 113 Test III Practice Problems sp 2011.tst

Math 113 Practice Problems Test III (Sections 6.1 - 6.5)
Spring 2011
Solve the triangle.
1)
75°
7
50°
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.
2) A = 26°
B = 23°
a = 49.8
3) A = 26°, B = 51°, c = 24
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.
4) B = 114°, b = 4, a = 25
5) B = 28°, b = 18.4, a = 19.6
6) A = 40°, a = 20 b = 15
7) A = 112°, a = 42..1, c = 37
A) B = 60°, C = 60°, c = 38.1
C) B = 13°, C = 55°, b = 10.2
B) B = 60°, C = 90°, c = 38.1
D) no triangle
Find the area of the triangle having the given measurements. Round to the nearest square unit.
8) A = 30°, b = 15 inches, c = 5 inches
9) C = 100°, a = 1 yards, b = 8 yards
Solve the problem.
10) A surveyor standing 52 meters from the base of a building measures the angle to the top of the building and
finds it to be 35°. The surveyor then measures the angle to the top of the radio tower on the building and finds
that it is 50°. How tall is the radio tower?
11) To find the distance AB across a river, a distance BC of 1221 m is laid off on one side of the river. It is found
that B = 110.8° and C = 13.7°. Find AB. Round to the nearest meter.
1
Find a. If necessary, round your answer to two decimal places.
12)
47°
37°
55
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.
13)
9
6
4
14) a = 6, c = 11, B = 107°
15) a = 8, b = 5, c = 4
Solve the problem.
16) Two airplanes leave an airport at the same time, one going northwest (bearing 135 °) at 409 mph and the other
going east at 325 mph. How far apart are the planes after 4 hours (to the nearest mile)?
17) A painter needs to cover a triangular region 60 meters by 69 meters by 70 meters. A can of paint covers 70
square meters. How many cans will be needed?
Use Heronʹs formula to find the area of the triangle. Round to the nearest square unit.
18) a = 16 yards, b = 13 yards, c = 16 yards
19) a = 12 meters, b = 18 meters, c = 7 meters
2
Use a polar coordinate system to plot the point with the given polar coordinates.
3π
20) (4, )
4
5
-5
5
-5
21) (-4, -3π
)
4
5
-5
5
-5
22) (4, -3π
)
4
5
-5
5
-5
3
Find another representation, (r, θ), for the point under the given conditions.
π
23) 1, , r > 0 and 2π < θ < 4π
3
24) 1, π
, r < 0 and 0 < θ < 2π
4
25) 9, π
, r > 0 and -2π < θ < 0
3
Polar coordinates of a point are given. Find the rectangular coordinates of the point.
2π
26) 9, 3
27) (-3, 120°)
The rectangular coordinates of a point are given. Find polar coordinates of the point.
28) (10, -10)
29) (2, -2)
The graph of a polar equation is given. Select the polar equation for the graph.
30)
5
4
3
2
1
-5
-4
-3
-2
-1
1
2
3
4
5 r
-1
-2
-3
-4
-5
A) r = 2
B) r = 2 sin(2θ)
C) r = 2 cos(2θ)
4
D) r = 2 + cos(2θ)
Graph the polar equation.
31) r = 1 + sin θ
6
5
4
3
2
1
1 2 3 4 5 6 r
-6 -5 -4 -3 -2 -1-1
-2
-3
-4
-5
-6
Plot the complex number.
32) 6 2 - 6 2i
i
10
5
-10
-5
5
10
R
-5
-10
Find the absolute value of the complex number.
33) z = 15i
34) z = 4 - 13i
Write the complex number in polar form. Express the argument in degrees.
35) 12 - 16i
Write the complex number in polar form. Express the argument in radians.
36) - 2 3 - 2i
Write the complex number in rectangular form.
37) 4(cos 211° + i sin 211°)
38) 7(cos 3π
3π
+ i sin )
4
4
5
Find the product of the complex numbers. Leave answer in polar form.
π
π
39) z 1 = 7(cos + i sin ) 4
4
z 2 = 4(cos 40) z 1 = 6(cos π
π
+ i sin )
6
6
3π
3π
+ i sin )
2
2
z 2 = 12(cos 5π
5π
+ i sin )
6
6
41) z 1 = 2 + 2i
z 2 = 3 - i
Find the quotient z1
z2
of the complex numbers. Leave answer in polar form.
1
5π
5π
42) z 1 = (cos + i sin )
8
4
4
π
π
1
z 2 = (cos + i sin )
6
6
3
43) z 1 = 5(cos 200° + i sin 200°)
z 2 = 4(cos 50° + i sin 50°)
Use DeMoivreʹs Theorem to find the indicated power of the complex number. Write answer in rectangular form.
44) 4(cos 15° + i sin 15°) 4
6
Answer Key
Testname: MATH 113 TEST III PRACTICE PROBLEMS SP 2011
1)
2)
3)
4)
5)
B = 55°, a = 6.55, c = 8.25
C = 131°, b = 44.4, c = 85.7
C = 103°, a = 10.8, b = 19.1
no triangle
A1 = 30°, C1 = 122°, c1 = 33.2;
22)
5
A2 = 150°, C2 = 2°, c2 = 1.4
6) B = 29°, C = 111°, c = 29.0
7) C
8) 19 square inches
9) 4 square yards
10) 25.56 meters
11) 351 meters
12) 17.53
13) A = 127.2°, B = 32.1°, C = 20.7°
14) b = 14, A = 24°, C = 49°
15) A = 125.1°, B = 30.8°, C = 24.1°
16) 2716 miles
17) 27 cans
18) 95 square yards
19) 25 square meters
20)
-5
-5
7
23) 1, π
3
5
24) -1, π
4
5
25) 9, - π
3
9 9 3
26) - , 2
2
5
27)
3 -3 3
, 2
2
28) 10 2, -5
5
7π
4
29) (-2 2, 135°)
30) C
31)
5
6
5
4
3
2
1
-5
21)
5
-6 -5 -4 -3 -2 -1-1
-2
-3
-4
-5
-6
-5
5
-5
7
1 2 3 4 5 6 r
Answer Key
Testname: MATH 113 TEST III PRACTICE PROBLEMS SP 2011
32)
i
10
5
-10
-5
5
10
R
-5
-10
33) 15
34) 185
35) 20(cos 306.9° + i sin 306.9°)
7π
7π
+ i sin 36) 4 cos 6
6
37) -3.4 - 2.1i
-7 2 7 2
38)
+ i
2
2
39) 28(cos 5π
5π
+ i sin )
12
12
40) 72(cos π
π
+ i sin )
3
3
41) 4 2(cos π
π
+ i sin )
12
12
42)
13π
13π
3
(cos + i sin )
12
12
8
43)
5
(cos 150° + i sin 150°)
4
44) 128 + 128 i 3
8