Question 1

Given   ,   , and   , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.

Accepted Answer

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

Question 2

Find the vector v that has a magnitude of   and is in the same direction as u, where   .

Accepted Answer

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

Question 3

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

Question 4

Plot the following complex number.

Accepted Answer

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

Question 5

Find the magnitude of vector v.

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Given   ,   , and   , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.

Accepted Answer

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

Question 8

Find the trigonometric form of the complex number represented graphically.

Accepted Answer

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

Question 9

Find the trigonometric form of the complex number shown below.

Accepted Answer

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

Question 10

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) 6.33 
B) 5.91 
C) 9.27 
D) 7.59 
E) 2.54 
A) 6.33 
B) 5.91 
C) 9.27 
D) 7.59 
E) 2.54

Question 11

Find all solutions to the following equation.

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Given   ,   , and   , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.

Accepted Answer

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

Question 14

Find the component form of v if   and the angle it makes with the x-axis is   .

Accepted Answer

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

Question 15

Given vectors   and   determine the quantity indicated below.

Accepted Answer

A) -6 
B) -21 
C) 36 
D) -18 
E) 78 
A) -6 
B) -21 
C) 36 
D) -18 
E) 78

Question 16

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 17

Let w be a vector with initial point   and terminal point   . Write w as a linear combination of the standard unit vectors i and j.

Accepted Answer

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

Question 18

Given   ,   , and   , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

Accepted Answer

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

Question 19

Find the absolute value of the complex number   .

Accepted Answer

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

Question 20

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

Accepted Answer

A)    
B) 13.71 
C) 12.25 
D) 7.88 
E) 11.16 
A)    
B) 13.71 
C) 12.25 
D) 7.88 
E) 11.16

Given , , and , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.

Find the vector v that has a magnitude of and is in the same direction as u, where .

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.

Plot the following complex number.

Find the magnitude of vector v.

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

Given , , and , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.

Find the trigonometric form of the complex number represented graphically.

Find the trigonometric form of the complex number shown below.

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.

Find all solutions to the following equation.

Given , , and , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.

Find the component form of v if and the angle it makes with the x-axis is .

Given vectors and determine the quantity indicated below.

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

Let w be a vector with initial point and terminal point . Write w as a linear combination of the standard unit vectors i and j.

Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

Find the absolute value of the complex number .

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

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

Given , , and , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.

Find the vector v that has a magnitude of and is in the same direction as u, where .

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.

Plot the following complex number.

Find the magnitude of vector v.

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

Given , , and , use the Law of Cosines to solve the triangle for the value of A. Round answer to two decimal places.

Find the trigonometric form of the complex number represented graphically.

Find the trigonometric form of the complex number shown below.

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.

Find all solutions to the following equation.

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

Given , , and , use the Law of Cosines to solve the triangle for the value of B. Round answer to two decimal places.

Find the component form of v if and the angle it makes with the x-axis is .

Given vectors and determine the quantity indicated below.

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

Let w be a vector with initial point and terminal point . Write w as a linear combination of the standard unit vectors i and j.

Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

Find the absolute value of the complex number .

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

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