Question 1

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

Accepted Answer

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

Question 2

Given vectors   and   determine the quantity indicated below.

Accepted Answer

A)  12 
B)  -112 
C)  -44 
D)  -48 
E)  -144 
A)  12 
B)  -112 
C)  -44 
D)  -48 
E)  -144

Question 3

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 4

Plot the following complex number.

Accepted Answer

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

Question 5

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.

Accepted Answer

A)  30.00 sq. units 
B)  27.00 sq. units 
C)  33.00 sq. units 
D)  36.00 sq. units 
E)  24.00 sq. units 
A)  30.00 sq. units 
B)  27.00 sq. units 
C)  33.00 sq. units 
D)  36.00 sq. units 
E)  24.00 sq. units

Question 6

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

Accepted Answer

A)  -324 
B)  729 
C)  324 
D)  2,916 
E)  243 
A)  -324 
B)  729 
C)  324 
D)  2,916 
E)  243

Question 7

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

Accepted Answer

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

Question 8

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 9

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 10

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 11

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 12

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 13

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.

Accepted Answer

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

Question 14

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)  12.33 
B)  17.78 
C)  13.69 
D)  23.24 
E)  15.06 
A)  12.33 
B)  17.78 
C)  13.69 
D)  23.24 
E)  15.06

Question 15

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 16

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]

Accepted Answer

A)    
B)    
C)    
D)  none of these 
E)    
A)    
B)    
C)    
D)  none of these 
E)

Question 17

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 6 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.

Accepted Answer

A)  3.49 feet 
B)  6.31 feet 
C)  5.71 feet 
D)  8.26 feet 
E)  4.15 feet 
A)  3.49 feet 
B)  6.31 feet 
C)  5.71 feet 
D)  8.26 feet 
E)  4.15 feet

Question 18

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

Accepted Answer

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

Question 19

Find the standard form of the complex number   . Round values to the nearest hundredth.

Accepted Answer

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

Question 20

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

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

Given vectors and determine the quantity indicated below.

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

Plot the following complex number.

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.

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 C. Round answer to two decimal places.

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

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.

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

Given vectors and determine the quantity indicated below.

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.

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

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

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]

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 6 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.

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

Find the standard form of the complex number . Round values to the nearest hundredth.

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.

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

Prerequisites

Filters

Exam 7: Additional Topics in Trigonometry

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

Given vectors and determine the quantity indicated below.

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

Plot the following complex number.

Determine the area of a triangle having the following measurements. Round your answer to two decimal places.

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 C. Round answer to two decimal places.

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

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.

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.

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

Given vectors and determine the quantity indicated below.

Use DeMoivre's Theorem to find the indicated power of the complex number. Write the result in standard form.

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

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

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]

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 6 feet long parallel to the road. Approximate the length of the pole. Round answer to two decimal places.

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

Find the standard form of the complex number . Round values to the nearest hundredth.

Determine where θ\thetaθ is the angle between u and v. 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

Prerequisites

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.