Question 1

Given vectors   and   , determine the quantity indicated below.

Accepted Answer

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

Question 2

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 3

Given   ,   , and   , use the Law of Sines to solve the triangle (if possible) for the value of b. 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 4

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 5

Given   ,   , and   , use the Law of Sines 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 6

Find the cube roots of the following complex number. Write each of the roots in standard form.-27

Accepted Answer

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

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

Find the angle between the vectors u and v if   and   . Round answer to two decimal places.

Accepted Answer

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

Question 9

Determine whether u and v are orthogonal, parallel, or neither.

Accepted Answer

A) orthogonal 
B) parallel 
C) neither 
A) orthogonal 
B) parallel 
C) neither

Question 10

Find the trigonometric form of the complex number shown below.

Accepted Answer

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

Question 11

Given   and   , find   .

Accepted Answer

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

Question 12

A force of   pounds is exerted along a rope attached to a crate at an angle of   above the horizontal. The crate is moved   feet. How much work has been accomplished? Round answer to one decimal place.

Accepted Answer

A)    foot-pounds 
B)    foot-pounds 
C)    foot-pounds 
D)    foot-pounds 
E)    foot-pounds 
A)    foot-pounds 
B)    foot-pounds 
C)    foot-pounds 
D)    foot-pounds 
E)    foot-pounds

Question 13

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 14

Find the trigonometric form of the complex number shown below.

Accepted Answer

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

Question 15

Find the projection of u onto v if   .

Accepted Answer

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

Question 16

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. Use dot products to determine the revenue for these two laptops if the price of each is increased by 7%.

Accepted Answer

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

Question 17

Find the component form of vector v with initial point   and terminal point   .

Accepted Answer

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

Question 18

Given   ,   , and   , use Heron's Area Formula to find the area of triangle   . Round answer to two decimal places.

Accepted Answer

A)    sq. units 
B)    sq. units 
C)    sq. units 
D)    sq. units 
E)    sq. units 
A)    sq. units 
B)    sq. units 
C)    sq. units 
D)    sq. units 
E)    sq. units

Question 19

Perform the indicated operation using trigonometric form. Leave answer in trigonometric form.

Accepted Answer

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

Question 20

Find all solutions to the following equation.

Accepted Answer

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

Given vectors and , determine the quantity indicated below.

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 (if possible) for the value of b. If two solutions exist, find both. 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.

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

Find the cube roots of the following complex number. Write each of the roots in standard form.-27

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

Find the angle between the vectors u and v if and . Round answer to two decimal places.

Determine whether u and v are orthogonal, parallel, or neither.

Find the trigonometric form of the complex number shown below.

Given and , find .

A force of pounds is exerted along a rope attached to a crate at an angle of above the horizontal. The crate is moved feet. How much work has been accomplished? Round answer to one decimal place.

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

Find the trigonometric form of the complex number shown below.

Find the projection of u onto v if .

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. Use dot products to determine the revenue for these two laptops if the price of each is increased by 7%.

Find the component form of vector v with initial point and terminal point .

Given , , and , use Heron's Area Formula to find the area of triangle . Round answer to two decimal places.

Perform the indicated operation using trigonometric form. Leave answer in trigonometric form.

Find all solutions to the following equation.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Filters

Exam 14: Additional Topics in Trigonometry

Given vectors and , determine the quantity indicated below.

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 (if possible) for the value of b. If two solutions exist, find both. 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.

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

Find the cube roots of the following complex number. Write each of the roots in standard form.-27

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

Find the angle between the vectors u and v if and . Round answer to two decimal places.

Determine whether u and v are orthogonal, parallel, or neither.

Find the trigonometric form of the complex number shown below.

Given and , find .

A force of pounds is exerted along a rope attached to a crate at an angle of above the horizontal. The crate is moved feet. How much work has been accomplished? Round answer to one decimal place.

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

Find the trigonometric form of the complex number shown below.

Find the projection of u onto v if .

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. Use dot products to determine the revenue for these two laptops if the price of each is increased by 7%.

Find the component form of vector v with initial point and terminal point .

Given , , and , use Heron's Area Formula to find the area of triangle . Round answer to two decimal places.

Perform the indicated operation using trigonometric form. Leave answer in trigonometric form.

Find all solutions to the following equation.

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Filters