Question 1

Find the product   using trigonometric forms. Leave the result in trigonometric form.

Accepted Answer

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

Question 2

Find the fourth roots of   Write the roots in trigonometric form.

Accepted Answer

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

Question 3

Determine   where $\theta$ is the angle between u and v. Round answer to two decimal places.

Accepted Answer

A) 7.07 
B) 5.00 
C) 6.83 
D) 8.66 
E) 6.04 
A) 7.07 
B) 5.00 
C) 6.83 
D) 8.66 
E) 6.04

Question 4

In the figure below,   ,   , and   . Use this information to solve the parallelogram for b. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

Accepted Answer

A) 6.79 
B) 12.92 
C) 14.97 
D) 11.39 
E) 10.88 
A) 6.79 
B) 12.92 
C) 14.97 
D) 11.39 
E) 10.88

Question 5

Write the complex number shown below in trigonometric form.

Accepted Answer

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

Question 6

Represent the complex number below graphically.

Accepted Answer

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

Question 7

Divide the complex numbers below and leave the result in trigonometric form.

Accepted Answer

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

Question 8

Find the cube roots of the following complex number. Write each of the roots in standard form.

Accepted Answer

A)    ,   ,   
B)    ,   
C)    
D)    ,   ,   
E)    ,   ,   
A)    ,   ,   
B)    ,   
C)    
D)    ,   ,   
E)    ,   ,

Question 9

Determine   where $\theta$ is the angle between u and v. Round answer to two decimal places.

Accepted Answer

A) 10.61 
B) 10.25 
C) 7.50 
D) 9.05 
E) 12.99 
A) 10.61 
B) 10.25 
C) 7.50 
D) 9.05 
E) 12.99

Question 10

Use the dot product to find the magnitude of u if

Accepted Answer

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

Question 11

A straight road makes an angle, A, of   with the horizontal. When the angle of elevation, B, of the sun is   , a vertical pole beside the road casts a shadow 8 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.

Accepted Answer

A) 10.20 feet 
B) 3.30 feet 
C) 6.27 feet 
D) 6.63 feet 
E) 12.32 feet 
A) 10.20 feet 
B) 3.30 feet 
C) 6.27 feet 
D) 6.63 feet 
E) 12.32 feet

Question 12

Perform the operation shown below and leave the result in trigonometric form.

Accepted Answer

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

Question 13

Use DeMoivre's Theorem to find the indicated power of the following complex number.

Accepted Answer

A)    
B) 32 
C) 64 
D) -64 
E)    
A)    
B) 32 
C) 64 
D) -64 
E)

Question 14

Given   , use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E) not possible 
A)    
B)    
C)    
D)    
E) not possible

Question 15

Perform the operation shown below and leave the result in trigonometric form.

Accepted Answer

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

Question 16

Represent the complex number below graphically.

Accepted Answer

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

Question 17

Given   and   , determine   .

Accepted Answer

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

Question 18

Perform the operation shown below and leave the result in trigonometric form.

Accepted Answer

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

Question 19

Find the trigonometric form of the complex number shown below.

Accepted Answer

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

Question 20

The vector   gives the number of units of two models of laptops produced by a company. The vector   gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by 5%.

Accepted Answer

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

Find the product using trigonometric forms. Leave the result in trigonometric form.

Find the fourth roots of Write the roots in trigonometric form.

Determine $Determine where \theta is the angle between u and v. Round answer to two decimal places.$ where $\theta$ is the angle between u and v. Round answer to two decimal places.

In the figure below, , , and . Use this information to solve the parallelogram for b. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

Write the complex number shown below in trigonometric form.

Represent the complex number below graphically.

Divide the complex numbers below and leave the result in trigonometric form.

Find the cube roots of the following complex number. Write each of the roots in standard form.

Determine $Determine where \theta is the angle between u and v. Round answer to two decimal places.$ where $\theta$ is the angle between u and v. Round answer to two decimal places.

Use the dot product to find the magnitude of u if

A straight road makes an angle, A, of with the horizontal. When the angle of elevation, B, of the sun is , a vertical pole beside the road casts a shadow 8 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.

Perform the operation shown below and leave the result in trigonometric form.

Use DeMoivre's Theorem to find the indicated power of the following complex number.

Given , use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.

Perform the operation shown below and leave the result in trigonometric form.

Represent the complex number below graphically.

Given and , determine .

Perform the operation shown below and leave the result in trigonometric form.

Find the trigonometric form of the complex number shown below.

The vector gives the number of units of two models of laptops produced by a company. The vector gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by 5%.

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Algebraic Expressions and Equations

Filters

Exam 7: Additional Topics in Trigonometry

Find the product using trigonometric forms. Leave the result in trigonometric form.

Find the fourth roots of Write the roots in trigonometric form.

Determine where θ\thetaθ is the angle between u and v. Round answer to two decimal places.

In the figure below, , , and . Use this information to solve the parallelogram for b. The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

Write the complex number shown below in trigonometric form.

Represent the complex number below graphically.

Divide the complex numbers below and leave the result in trigonometric form.

Find the cube roots of the following complex number. Write each of the roots in standard form.

Determine where θ\thetaθ is the angle between u and v. Round answer to two decimal places.

Use the dot product to find the magnitude of u if

A straight road makes an angle, A, of with the horizontal. When the angle of elevation, B, of the sun is , a vertical pole beside the road casts a shadow 8 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.

Perform the operation shown below and leave the result in trigonometric form.

Use DeMoivre's Theorem to find the indicated power of the following complex number.

Given , use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.

Perform the operation shown below and leave the result in trigonometric form.

Represent the complex number below graphically.

Given and , determine .

Perform the operation shown below and leave the result in trigonometric form.

Find the trigonometric form of the complex number shown below.

The vector gives the number of units of two models of laptops produced by a company. The vector gives the prices (in dollars) of the two models of laptops, respectively. Identify the vector operation used to increase revenue by 5%.

Functions and Their Graphs

Solving Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Algebraic Expressions and Equations

Filters

Determine $Determine where \theta is the angle between u and v. Round answer to two decimal places.$ where $\theta$ is the angle between u and v. Round answer to two decimal places.

Determine $Determine where \theta is the angle between u and v. Round answer to two decimal places.$ where $\theta$ is the angle between u and v. Round answer to two decimal places.