Question 1

Use De Moivre's theorem to simplify the expression. Write the answer in a + bi form.
-

Accepted Answer

A)  -64 
B)    
C)    
D)  64i 
A)  -64 
B)    
C)    
D)  64i

Question 2

Solve the problem.
-A projectile is fired with an initial velocity of 300 feet per second at an angle of 70° with the horizontal. In how many seconds will the projectile reach its maximum altitude? (Round your answer to the nearest tenth of a
Second.) The parametric equations for the path of the projectile are

Accepted Answer

A)  5.4 seconds 
B)  8.8 seconds 
C)  13.6 seconds 
D)  16.9 seconds 
A)  5.4 seconds 
B)  8.8 seconds 
C)  13.6 seconds 
D)  16.9 seconds

Question 3

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].
-

Accepted Answer

A)  40; 45° 
B)    
C)  20; 45° 
D)  20; 225° 
A)  40; 45° 
B)    
C)  20; 45° 
D)  20; 225°

Question 4

Solve the problem.
-Suppose you would like to cross a 210-foot wide river in a boat. Assume that the boat can travel 37 mph relative to the water and that the current is flowing west at the rate of 7 mph. If the bearing is chosen so that the
Boat will land at a point exactly across from its starting point, how long will it take for the boat to make the
Crossing? Give your answer to the nearest second.

Accepted Answer

A)  16 sec 
B)  2 sec 
C)  4 sec 
D)  8 sec 
A)  16 sec 
B)  2 sec 
C)  4 sec 
D)  8 sec

Question 5

Write the complex number in trigonometric form, using degree measure for the argument.
--5

Accepted Answer

A)  5(cos 270° + i sin 270°) 
B)  5(cos 90° + i sin 90°) 
C)  5(cos 180° + i sin 180°) 
D)  5(cos 0° + i sin 0°) 
A)  5(cos 270° + i sin 270°) 
B)  5(cos 90° + i sin 90°) 
C)  5(cos 180° + i sin 180°) 
D)  5(cos 0° + i sin 0°)

Question 6

State if the vectors a and b are perpendicular, parallel, or neither. If a and b are parallel, state whether they point in the
same direction or in opposite directions.
-a = 8, 10 , b = 32, 40

Accepted Answer

A)  Parallel, opposite directions 
B)  Parallel, same direction 
C)  Perpendicular 
D)  Neither 
A)  Parallel, opposite directions 
B)  Parallel, same direction 
C)  Perpendicular 
D)  Neither

Question 7

Change the polar coordinates   to rectangular coordinates (x, y).
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 8

Solve.
-Two points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 70 yd from B and 103 yd from A, with angle ACB measuring 69.3°. How far apart are A and B (to the nearest yard)?

Accepted Answer

A)  120 yd 
B)  129 yd 
C)  102 yd 
D)  111 yd 
A)  120 yd 
B)  129 yd 
C)  102 yd 
D)  111 yd

Question 9

Solve.
-Two forces of 250 and 70 N (newtons) act on an object at right angles. Find the magnitude of the resultant and the angle that it makes with the larger force.

Accepted Answer

A)  260 N, 6° 
B)  67,400 N, 16° 
C)  260 N, 74° 
D)  260 N, 16° 
A)  260 N, 6° 
B)  67,400 N, 16° 
C)  260 N, 74° 
D)  260 N, 16°

Question 10

Write the complex number in trigonometric form, using degree measure for the argument.
-15 - 20i

Accepted Answer

A)  25(cos 306.9° + i sin 306.9°) 
B)  25(cos 126.9° + i sin 126.9°) 
C)  25(cos 233.1° + i sin 233.1°) 
D)  25(cos 53.1° + i sin 53.1°) 
A)  25(cos 306.9° + i sin 306.9°) 
B)  25(cos 126.9° + i sin 126.9°) 
C)  25(cos 233.1° + i sin 233.1°) 
D)  25(cos 53.1° + i sin 53.1°)

Question 11

Use De Moivre's theorem to simplify the expression. Write the answer in a + bi form.
-

Accepted Answer

A)  -32 + 32i 
B)  -32i 
C)  32 
D)  32 - 32i 
A)  -32 + 32i 
B)  -32i 
C)  32 
D)  32 - 32i

Question 12

Write the complex number in the form a + bi.
-8(cos 30° + i sin 30°)

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 13

Graph the point.
-

Accepted Answer

A)    
B)    
A)    
B)

Question 14

Solve.
-To find the distance between two small towns, an electronic distance measuring (EDM) instrument is placed on a hill from which both towns are visible. The distance from the EDM to the towns is 2.6 miles and 2.7 miles and
The angle between the two lines of sight is 41°. Find the distance between the towns to the nearest tenth of a
Mile.

Accepted Answer

A)  5.0 mi 
B)  1.9 mi 
C)  4.4 mi 
D)  3.0 mi 
A)  5.0 mi 
B)  1.9 mi 
C)  4.4 mi 
D)  3.0 mi

Question 15

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].
-

Accepted Answer

A)  14; 344.5° 
B)  14; 105.5° 
C)    
D)    
A)  14; 344.5° 
B)  14; 105.5° 
C)    
D)

Question 16

Find the magnitude of the horizontal and the vertical components for the vector with the given magnitude and direction
angle   Round to the nearest tenth.
-

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

Perform the indicated operation. Use the form for vectors. -v = <1, -7>, w = <-6, -3>, u = <-9, -1>; Find v + w - 7u.

Accepted Answer

A) <58, -3> B) <-6, -9, 70> C) <-15, 70> D) <-14, -11> A) <58, -3> B) <-6, -9, 70> C) <-15, 70> D) <-14, -11>

Question 18

Approximate the area of the triangle to the nearest tenth.
-18.8
12.6
17.0

Accepted Answer

A)  104 
B)  113 
C)  110 
D)  107 
A)  104 
B)  113 
C)  110 
D)  107

Question 19

Solve the problem.
-A pilot wants to fly on a bearing of 61.1°. By flying due east, he finds that a 50-mph wind, blowing from the south, puts him on course. Find the airspeed of the plane to the nearest mile per hour.

Accepted Answer

A)  136 mph 
B)  45 mph 
C)  91 mph 
D)  103 mph 
A)  136 mph 
B)  45 mph 
C)  91 mph 
D)  103 mph

Question 20

For the point given in rectangular coordinates, find equivalent polar coordinates  
-(-6, -6)

Accepted Answer

A)    
B)  (-6, 225°) 
C)  (-12, 315°) 
D)    
A)    
B)  (-6, 225°) 
C)  (-12, 315°) 
D)

Use De Moivre's theorem to simplify the expression. Write the answer in a + bi form. -

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. -

Write the complex number in trigonometric form, using degree measure for the argument. --5

State if the vectors a and b are perpendicular, parallel, or neither. If a and b are parallel, state whether they point in the same direction or in opposite directions. -a = 8, 10 , b = 32, 40

Change the polar coordinates to rectangular coordinates (x, y). -

Solve. -Two points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 70 yd from B and 103 yd from A, with angle ACB measuring 69.3°. How far apart are A and B (to the nearest yard)?

Solve. -Two forces of 250 and 70 N (newtons) act on an object at right angles. Find the magnitude of the resultant and the angle that it makes with the larger force.

Write the complex number in trigonometric form, using degree measure for the argument. -15 - 20i

Use De Moivre's theorem to simplify the expression. Write the answer in a + bi form. -

Write the complex number in the form a + bi. -8(cos 30° + i sin 30°)

Graph the point. -

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. -

Find the magnitude of the horizontal and the vertical components for the vector with the given magnitude and direction angle Round to the nearest tenth. -

Perform the indicated operation. Use the form <a, b> for vectors. -v = <1, -7>, w = <-6, -3>, u = <-9, -1>; Find v + w - 7u.

Approximate the area of the triangle to the nearest tenth. -18.8 12.6 17.0

Solve the problem. -A pilot wants to fly on a bearing of 61.1°. By flying due east, he finds that a 50-mph wind, blowing from the south, puts him on course. Find the airspeed of the plane to the nearest mile per hour.

For the point given in rectangular coordinates, find equivalent polar coordinates -(-6, -6)

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Exam 7: Applications of Trigonometry

Use De Moivre's theorem to simplify the expression. Write the answer in a + bi form. -

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. -

Write the complex number in trigonometric form, using degree measure for the argument. --5

State if the vectors a and b are perpendicular, parallel, or neither. If a and b are parallel, state whether they point in the same direction or in opposite directions. -a = 8, 10 , b = 32, 40

Change the polar coordinates to rectangular coordinates (x, y). -

Solve. -Two points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 70 yd from B and 103 yd from A, with angle ACB measuring 69.3°. How far apart are A and B (to the nearest yard)?

Solve. -Two forces of 250 and 70 N (newtons) act on an object at right angles. Find the magnitude of the resultant and the angle that it makes with the larger force.

Write the complex number in trigonometric form, using degree measure for the argument. -15 - 20i

Use De Moivre's theorem to simplify the expression. Write the answer in a + bi form. -

Write the complex number in the form a + bi. -8(cos 30° + i sin 30°)

Graph the point. -

Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an angle in [0,360°]. -

Find the magnitude of the horizontal and the vertical components for the vector with the given magnitude and direction angle Round to the nearest tenth. -

Perform the indicated operation. Use the form <a, b> for vectors. -v = <1, -7>, w = <-6, -3>, u = <-9, -1>; Find v + w - 7u.

Approximate the area of the triangle to the nearest tenth. -18.8 12.6 17.0

Solve the problem. -A pilot wants to fly on a bearing of 61.1°. By flying due east, he finds that a 50-mph wind, blowing from the south, puts him on course. Find the airspeed of the plane to the nearest mile per hour.

For the point given in rectangular coordinates, find equivalent polar coordinates -(-6, -6)

Equations, Inequalities, and Modeling

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

The Trigonometric Functions

Trigonometric Identities and Conditional Equations

Systems of Equations and Inequalities

Matrices and Determinants

The Conic Sections

Sequences, Series, and Probability

Basic Algebra Review

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