Question 1

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

Accepted Answer

A)  2048 
B)    
C)  -4,096 
D)    
E)  4,096 
A)  2048 
B)    
C)  -4,096 
D)    
E)  4,096 E

Question 2

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)    B

Question 3

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 5.5%.

Accepted Answer

A)  $10,701,150 
B)  $10,852,400 
C)  $11,003,650 
D)  $10,732,500 
E)  $10,812,433 
A)  $10,701,150 
B)  $10,852,400 
C)  $11,003,650 
D)  $10,732,500 
E)  $10,812,433 C

Question 4

Find the magnitude and direction angle of   .

Accepted Answer

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

Question 5

A force of 45 pounds is exerted along a rope attached to a crate at an angle of 30° above the horizontal. The crate is moved 23 feet. How much work has been accomplished? Round answer to one decimal place.

Accepted Answer

A)  965.7 foot-pounds 
B)  1,035.0 foot-pounds 
C)  1,195.1 foot-pounds 
D)  896.3 foot-pounds 
E)  1,080.4 foot-pounds 
A)  965.7 foot-pounds 
B)  1,035.0 foot-pounds 
C)  1,195.1 foot-pounds 
D)  896.3 foot-pounds 
E)  1,080.4 foot-pounds

Question 6

Find the component form of vector v.

Accepted Answer

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

Question 7

Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of   at 15 miles per hour, and the other travels at a bearing of   at 17 miles per hour. Approximate the distance between them at noon the same day. Round answer to two decimal places.

Accepted Answer

A)  44.71 miles 
B)  23.86 miles 
C)  30.37 miles 
D)  27.02 miles 
E)  39.96 miles 
A)  44.71 miles 
B)  23.86 miles 
C)  30.37 miles 
D)  27.02 miles 
E)  39.96 miles

Question 8

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 9

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 10

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 11

A vertical pole 29 feet tall stands on a hillside that makes an angle of   with the horizontal. Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 78 feet downhill from the base of the pole. Round answer to two decimal places.

Accepted Answer

A)  82.88 feet 
B)  75.35 feet 
C)  99.45 feet 
D)  88.40 feet 
E)    feet 
A)  82.88 feet 
B)  75.35 feet 
C)  99.45 feet 
D)  88.40 feet 
E)    feet

Question 12

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

Accepted Answer

A)  17.36 sq. units 
B)  18.44 sq. units 
C)  20.21 sq. units 
D)  16.76 sq. units 
E)  14.02 sq. units 
A)  17.36 sq. units 
B)  18.44 sq. units 
C)  20.21 sq. units 
D)  16.76 sq. units 
E)  14.02 sq. units

Question 13

Find the component form of v if   and the angle it makes with the x-axis is 150°.

Accepted Answer

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

Question 14

A park ranger at point A observes a fire in the direction   . Another ranger at point B, 5 miles due east of A, sites the same fire at   . Determine the distance from point B to the fire. Round answer to two decimal places.

Accepted Answer

A)  2.18 miles 
B)  4.55 miles 
C)  2.51 miles 
D)  4.84 miles 
E)  4.20 miles 
A)  2.18 miles 
B)  4.55 miles 
C)  2.51 miles 
D)  4.84 miles 
E)  4.20 miles

Question 15

After a severe storm, three sisters, April, May, and June, stood on their front porch and noticed that the tree in their front yard was leaning   from vertical toward the house. From the porch, which is 98 feet away from the base of the tree, they noticed that the angle of elevation to the top of the tree was   . Approximate the height of the tree. Round answer to two decimal places.

Accepted Answer

A)  47.99 feet 
B)  56.03 feet 
C)  41.91 feet 
D)  45.31 feet 
E)  46.03 feet 
A)  47.99 feet 
B)  56.03 feet 
C)  41.91 feet 
D)  45.31 feet 
E)  46.03 feet

Question 16

Find the standard form of the complex number shown below. Round answers to two decimal places.

Accepted Answer

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

Question 17

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)  16.29 
B)  11.26 
C)  15.57 
D)  17.00 
E)  14.13 
A)  16.29 
B)  11.26 
C)  15.57 
D)  17.00 
E)  14.13

Question 18

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)  a= 14.57 
B)  a= 13.14 
C)  a= 11.24 
D)  a= 13.69 
E)  a= 12.46 
A)  a= 14.57 
B)  a= 13.14 
C)  a= 11.24 
D)  a= 13.69 
E)  a= 12.46

Question 19

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

Accepted Answer

A)  3,125 
B)  62,500 
C)  15,625 
D)  2,500 
E)  -2,500 
A)  3,125 
B)  62,500 
C)  15,625 
D)  2,500 
E)  -2,500

Question 20

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)

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

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

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 5.5%.

Find the magnitude and direction angle of .

A force of 45 pounds is exerted along a rope attached to a crate at an angle of 30° above the horizontal. The crate is moved 23 feet. How much work has been accomplished? Round answer to one decimal place.

Find the component form of vector v.

Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of at 15 miles per hour, and the other travels at a bearing of at 17 miles per hour. Approximate the distance between them at noon the same day. Round answer to two decimal places.

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

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

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

A vertical pole 29 feet tall stands on a hillside that makes an angle of with the horizontal. Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 78 feet downhill from the base of the pole. Round answer to two decimal places.

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

Find the component form of v if and the angle it makes with the x-axis is 150°.

A park ranger at point A observes a fire in the direction . Another ranger at point B, 5 miles due east of A, sites the same fire at . Determine the distance from point B to the fire. Round answer to two decimal places.

Find the standard form of the complex number shown below. Round answers 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.

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

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

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Polynomial Functions

Rational Functions and Conics

Exponential and Logarithmic Functions

Analytic Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Filters

Exam 8: Additional Topics in Trigonometry

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

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

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 5.5%.

Find the magnitude and direction angle of .

A force of 45 pounds is exerted along a rope attached to a crate at an angle of 30° above the horizontal. The crate is moved 23 feet. How much work has been accomplished? Round answer to one decimal place.

Find the component form of vector v.

Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of at 15 miles per hour, and the other travels at a bearing of at 17 miles per hour. Approximate the distance between them at noon the same day. Round answer to two decimal places.

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

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

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

A vertical pole 29 feet tall stands on a hillside that makes an angle of with the horizontal. Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 78 feet downhill from the base of the pole. Round answer to two decimal places.

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

Find the component form of v if and the angle it makes with the x-axis is 150°.

A park ranger at point A observes a fire in the direction . Another ranger at point B, 5 miles due east of A, sites the same fire at . Determine the distance from point B to the fire. Round answer to two decimal places.

Find the standard form of the complex number shown below. Round answers 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.

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

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

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Polynomial Functions

Rational Functions and Conics

Exponential and Logarithmic Functions

Analytic Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Filters