Question 1

For the given polar equation, write an equivalent rectangular equation.
-r = 5

Accepted Answer

A)    
B)  x + y = 25 
C)    
D)  x + y = 5 
A)    
B)  x + y = 25 
C)    
D)  x + y = 5

Question 2

Eliminate the parameter of the pair of parametric equations.
-x = 3t, y = t + 7

Accepted Answer

A)    
B)  y = 3x - 7 
C)  y = 3x + 7 
D)    
A)    
B)  y = 3x - 7 
C)  y = 3x + 7 
D)

Question 3

Solve the problem.
-A projectile is fired from a height of 8.4 feet with an initial velocity of 196 ft/sec at an angle of 49° with the horizontal. The parametric equations for the path of the projectile are   where x and y are in feet and t is in seconds. Find the height of the projectile after 4 seconds. Round your
Answer to the nearest tenth of a foot.

Accepted Answer

A)  536.1 ft 
B)  344.1 ft 
C)  335.7 ft 
D)  514.4 ft 
A)  536.1 ft 
B)  344.1 ft 
C)  335.7 ft 
D)  514.4 ft

Question 4

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

Accepted Answer

A)  -724.077 - 724.077i 
B)  -2.828 - 2.828i 
C)  2.828 - 2.828i 
D)  724.077 - 724.077i 
A)  -724.077 - 724.077i 
B)  -2.828 - 2.828i 
C)  2.828 - 2.828i 
D)  724.077 - 724.077i

Question 5

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

Accepted Answer

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

Question 6

Solve the triangle. Approximate values to the nearest tenth when appropriate.
-  = 116.1° a = 6.40
B = 11.77

Accepted Answer

A)    
B)  No solution 
C)    
D)    
A)    
B)  No solution 
C)    
D)

Question 7

Change the polar coordinates   to rectangular coordinates (x, y).
-(-4, 90°)

Accepted Answer

A)  (4, 0) 
B)  (0, -4) 
C)  (-4, 0) 
D)  (0, 4) 
A)  (4, 0) 
B)  (0, -4) 
C)  (-4, 0) 
D)  (0, 4)

Question 8

Determine the number of triangles with the given parts.
-a = 35, b = 46,   = 26°

Accepted Answer

A)  0 
B)  3 
C)  2 
D)  1 
A)  0 
B)  3 
C)  2 
D)  1

Question 9

Find all specified roots.
-Fourth roots of -16

Accepted Answer

A)  1 + i, 1 - i, -1 + i, -1 - i 
B)    
C)  2 + i, 2 - i, -2 + i, -2 - i 
D)    
A)  1 + i, 1 - i, -1 + i, -1 - i 
B)    
C)  2 + i, 2 - i, -2 + i, -2 - i 
D)

Question 10

Use a calculator to convert from polar to rectangular coordinates. Round to the nearest hundredth.
-(3.4, 44°)

Accepted Answer

A)  (2.36, 2.45) 
B)  (0.72, 0.69) 
C)  (-2.45, -2.36) 
D)  (2.45, 2.36) 
A)  (2.36, 2.45) 
B)  (0.72, 0.69) 
C)  (-2.45, -2.36) 
D)  (2.45, 2.36)

Question 11

Solve the problem.
-A projectile is fired from a height of 7.4 feet with an initial velocity of 127 ft/sec at an angle of 59° with the horizontal. The parametric equations for the path of the projectile are   where x and y are in feet and t is in seconds. How long does it take the projectile to hit the ground? Round your
Answer to the nearest tenth of a second.

Accepted Answer

A)  6.8 seconds 
B)  13.7 seconds 
C)  6.9 seconds 
D)  8.8 seconds 
A)  6.8 seconds 
B)  13.7 seconds 
C)  6.9 seconds 
D)  8.8 seconds

Question 12

Solve.
-Two forces of 330 and 250 N (newtons) act on an object. The angle between the forces is 15°. Find the magnitude of the resultant and the angle that it makes with the larger force.

Accepted Answer

A)  4 N, 6° 
B)  574 N, 6° 
C)  576 N, 6° 
D)  575 N, 6° 
A)  4 N, 6° 
B)  574 N, 6° 
C)  576 N, 6° 
D)  575 N, 6°

Question 13

Solve the problem.
-One rope pulls a barge directly east with a force of 77 N, and another rope pulls the barge directly north with a force of 44 N. Find the magnitude of the resultant force acting on the barge. Round to the nearest Newton.

Accepted Answer

A)  33 N 
B)  3400 N 
C)  121 N 
D)  89 N 
A)  33 N 
B)  3400 N 
C)  121 N 
D)  89 N

Question 14

Perform the indicated operation. Write the answer in the form a + bi.
-

Accepted Answer

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

Question 15

Find the indicated roots. Write the answer in trigonometric form.
-Cube roots of 125(cos 276° + i sin 276°)

Accepted Answer

A)  5(cos 92° + i sin 92°), 5(cos 152° + i sin 152°), 5(cos 32° + i sin 32°) 
B)  5(cos 182° + i sin 182°), 5(cos 242° + i sin 242°), 5(cos 122° + i sin 122°) 
C)  5(cos 92° + i sin 92°), 5(cos 212° + i sin 212°), 5(cos 212° + i sin 212°) 
D)  5(cos 92° + i sin 92°), 5(cos 212° + i sin 212°), 5(cos 332° + i sin 332°) 
A)  5(cos 92° + i sin 92°), 5(cos 152° + i sin 152°), 5(cos 32° + i sin 32°) 
B)  5(cos 182° + i sin 182°), 5(cos 242° + i sin 242°), 5(cos 122° + i sin 122°) 
C)  5(cos 92° + i sin 92°), 5(cos 212° + i sin 212°), 5(cos 212° + i sin 212°) 
D)  5(cos 92° + i sin 92°), 5(cos 212° + i sin 212°), 5(cos 332° + i sin 332°)

Question 16

Find the component form for the vector with the given magnitude and direction angle   . Round values to the nearest
tenth.
-

Accepted Answer

A)  113.8, 26.5 
B)  -26.5, 113.8 
C)  113.8, -26.5 
D)  26.5, 113.8 
A)  113.8, 26.5 
B)  -26.5, 113.8 
C)  113.8, -26.5 
D)  26.5, 113.8

Question 17

Find the magnitude and direction angle of the resultant.
-

Accepted Answer

A)  16, 114.4° 
B)    
C)    
D)    
A)  16, 114.4° 
B)    
C)    
D)

Question 18

The vectors u, v, and w are drawn below. Sketch the given vector.  
-u - v

Accepted Answer

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

Question 19

Perform the operation on the given vectors and find the magnitude and direction angle for the new vector.
-Given A = 3, 4 and B = -2, 6 A + B

Accepted Answer

A)  11, 84.8° 
B)  10, 95.7° 
C)    
D)    
A)  11, 84.8° 
B)  10, 95.7° 
C)    
D)

Question 20

Perform the indicated operation. Write the answer in the form a + bi.
-7(cos 60° + i sin 60°) · 2(cos 90° + i sin 90°)

Accepted Answer

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

For the given polar equation, write an equivalent rectangular equation. -r = 5

Eliminate the parameter of the pair of parametric equations. -x = 3t, y = t + 7

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

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

Solve the triangle. Approximate values to the nearest tenth when appropriate. - = 116.1° a = 6.40 B = 11.77

Change the polar coordinates to rectangular coordinates (x, y). -(-4, 90°)

Determine the number of triangles with the given parts. -a = 35, b = 46, = 26°

Find all specified roots. -Fourth roots of -16

Use a calculator to convert from polar to rectangular coordinates. Round to the nearest hundredth. -(3.4, 44°)

Solve. -Two forces of 330 and 250 N (newtons) act on an object. The angle between the forces is 15°. Find the magnitude of the resultant and the angle that it makes with the larger force.

Solve the problem. -One rope pulls a barge directly east with a force of 77 N, and another rope pulls the barge directly north with a force of 44 N. Find the magnitude of the resultant force acting on the barge. Round to the nearest Newton.

Perform the indicated operation. Write the answer in the form a + bi. -

Find the indicated roots. Write the answer in trigonometric form. -Cube roots of 125(cos 276° + i sin 276°)

Find the component form for the vector with the given magnitude and direction angle . Round values to the nearest tenth. -

Find the magnitude and direction angle of the resultant. -

The vectors u, v, and w are drawn below. Sketch the given vector. -u - v

Perform the operation on the given vectors and find the magnitude and direction angle for the new vector. -Given A = 3, 4 and B = -2, 6 A + B

Perform the indicated operation. Write the answer in the form a + bi. -7(cos 60° + i sin 60°) · 2(cos 90° + i sin 90°)

Equations, Inequalities, and Modeling

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Exam 7: Applications of Trigonometry

For the given polar equation, write an equivalent rectangular equation. -r = 5

Eliminate the parameter of the pair of parametric equations. -x = 3t, y = t + 7

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

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

Solve the triangle. Approximate values to the nearest tenth when appropriate. - = 116.1° a = 6.40 B = 11.77

Change the polar coordinates to rectangular coordinates (x, y). -(-4, 90°)

Determine the number of triangles with the given parts. -a = 35, b = 46, = 26°

Find all specified roots. -Fourth roots of -16

Use a calculator to convert from polar to rectangular coordinates. Round to the nearest hundredth. -(3.4, 44°)

Solve. -Two forces of 330 and 250 N (newtons) act on an object. The angle between the forces is 15°. Find the magnitude of the resultant and the angle that it makes with the larger force.

Solve the problem. -One rope pulls a barge directly east with a force of 77 N, and another rope pulls the barge directly north with a force of 44 N. Find the magnitude of the resultant force acting on the barge. Round to the nearest Newton.

Perform the indicated operation. Write the answer in the form a + bi. -

Find the indicated roots. Write the answer in trigonometric form. -Cube roots of 125(cos 276° + i sin 276°)

Find the component form for the vector with the given magnitude and direction angle . Round values to the nearest tenth. -

Find the magnitude and direction angle of the resultant. -

The vectors u, v, and w are drawn below. Sketch the given vector. -u - v

Perform the operation on the given vectors and find the magnitude and direction angle for the new vector. -Given A = 3, 4 and B = -2, 6 A + B

Perform the indicated operation. Write the answer in the form a + bi. -7(cos 60° + i sin 60°) · 2(cos 90° + i sin 90°)

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

Filters