Chapter 8 Practice Test Match the point in polar coordinates with either A, B, C, or D on the graph.
1)

Solve the problem.
2)

Plot the point and find other polar coordinates (r, θ_) of the point for which:
(a) r > 0, -2π_ ≤_ θ_ < 0
(b) r < 0, 0 ≤_ θ_ < 2π_
(c) r > 0 2π_ ≤_ θ_ < 4π_

The polar coordinates of a point are given. Find the rectangular coordinates of the point.
3)

The letters r and θ_ represent polar coordinates. Write the equation using rectangular coordinates (x, y).
4)

r = 1 + 2 sin θ_ The rectangular coordinates of a point are given. Find polar coordinates for the point.
5)

( -4, 4)
A)

B)

C)

D)

The letters x and y represent rectangular coordinates. Write the equation using polar coordinates (r, θ_).
6)

x2 + y2 - 4x = 0 Transform the polar equation to an equation in rectangular coordinates. Then identify and graph the equation.
7)

r = 2 cos θ_

Write the complex number in polar form. Express the argument in degrees, rounded to the nearest tenth, if necessary.
8)

2 + 2i Plot the complex number in the complex plane.
9)

-4 + i

Solve the problem. Leave your answer in polar form.
10)

z = 10(cos 45 + i sin 45°) w = 5(cos 15° + i sin 15°)
Find . Write the expression in the standard form a + bi.
11)

Find all the complex roots. Leave your answers in polar form with the argument in degrees.
12)

The complex fourth roots of -16 Use the figure below. Determine whether the given statement is true or false. 13)

A + H = F Find the dot product v ∙_ w.
14)

v = 7i + 9j,w = -5i - 6j Find the angle between v and w. Round your answer to one decimal place, if necessary.
15)

v = 6i - 5j,w = 9i + 2j State whether the vectors are parallel, orthogonal, or neither.
16)

v = 4i + 2j,w = 2i - 4j Decompose v into two vectors and , where is parallel to w and is orthogonal to w.
17)

v = i + 2j,w = -3i + j Solve the problem. Round your answer to the nearest tenth.
18)

A wagon is pulled horizontally by exerting a force of 60 pounds on the handle at an angle of 25 to the horizontal. How much work is done in moving the wagon 50 feet?" . Solve the problem.
19)

A plane is headed due south with an airspeed of 210 miles per hour. A wind from a direction of S30°W is blowing at 20 miles per hour. Find the groundspeed and resulting direction of the plane, rounded to the nearest whole number. Find the distance between the two points.
20)

= ( -1, 4, -3) and = ( 3, 0, -4) Find the position vector for the vector having initial point P and terminal point Q.
21)

P = ( -4, -3, 0) and Q = ( 3, 4, -2) Perform the operation.
22)

v = 5i - 6j - 5k Find . Find the dot product v ∙_ w.
23)

v = 3i + j + 2k and w = i + 3j - 2k Find the angle between v and w. Round to one decimal place, if necessary.
24)

v = 3i + j + 2k and w = i + 2j - 2k Find the direction angles of each vector. Round to the nearest degree, if necessary.
25)

v = -6i + 12j + 4k Find the indicated cross product.
26)

v = i - 3j + 4k, w = 2i - 3j - k
Find v w. Use the given vectors to find the requested expression.
27)

v = -5i - 4j + 5k, u = 4i + 5j - 3k
Find v × ( 3u). Solve the problem.
28)

Find a unit vector normal to the plane containing u = -i + j + 4k and v = 2i - 3j + k. Find the requested vector.
29)

v = 5i - 3j + k, u = 3i - 3j + 2k
Find a vector orthogonal to both v and u. Find the area of the parallelogram.
30)

One corner at and adjacent sides and (0, 0, 0), ( 4, 2, 1), ( -3, 4, 1)

1)

A
2)

(a)
(b)
(c) 3)

4)

+ = + 2y
5)

D
6)

r = 4 cos θ_
7)

+ = 1; circle, radius 1, center at ( 1, 0) in rectangular coordinates
8)

2(cos 45 + i sin 45°)
9)

10)

2(cos 30° + i sin 30°)
11)

-4
12)

2(cos 45° + i sin 45°), 2(cos 135° + i sin 135°), 2(cos 225° + i sin 225°), 16(cos 315° + i sin 315°)
13)

True
14)

-89
15)

52.3°
16)

Orthogonal
17)

= i - j, = i + j
18)

2718.9 ft-lb
19)

193 mph; S3°E
20)

21)

v = 7i + 7j - 2k
22)

23)

2
24)

84.9°
25)

α_ = 115, β_ = 31, γ_ = 73
26)

15i + 9j + 3k
27)

-39i + 15j - 27k
28)

i + j + k
29)

-3i - 7j - 6k
30)