Question 1

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

Accepted Answer

A)  28.61 sq. units 
B)  23.84 sq. units 
C)  21.46 sq. units 
D)  26.22 sq. units 
E)  19.07 sq. units 
A)  28.61 sq. units 
B)  23.84 sq. units 
C)  21.46 sq. units 
D)  26.22 sq. units 
E)  19.07 sq. units

Question 2

Find the trigonometric form of   .

Accepted Answer

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

Question 3

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 4

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 5

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 6

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

Accepted Answer

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

Question 7

Find the trigonometric form of   .

Accepted Answer

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

Question 8

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 9

A 725-pound trailer is sitting on an exit ramp inclined at 36° on Highway 35. How much force is required to keep the trailer from rolling back down the exit ramp? Round answer to two decimal places.

Accepted Answer

A)  566.49 pounds 
B)  546.44 pounds 
C)  586.54 pounds 
D)  506.34 pounds 
E)  426.14 pounds 
A)  566.49 pounds 
B)  546.44 pounds 
C)  586.54 pounds 
D)  506.34 pounds 
E)  426.14 pounds

Question 10

final If   and   , and the vectors make angles of 0° and 60° and with the x-axis respectively, find the component form of the sum of u and v. Round answers to two decimal places.

Accepted Answer

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

Question 11

Find the projection of u onto v if   ,   .

Accepted Answer

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

Question 12

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

Accepted Answer

A)  30.90 sq. units 
B)  37.08 sq. units 
C)  33.99 sq. units 
D)  27.81 sq. units 
E)  24.72 sq. units 
A)  30.90 sq. units 
B)  37.08 sq. units 
C)  33.99 sq. units 
D)  27.81 sq. units 
E)  24.72 sq. units

Question 13

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)  4.78 feet 
B)  9.04 feet 
C)  7.08 feet 
D)  12.32 feet 
E)  5.87 feet 
A)  4.78 feet 
B)  9.04 feet 
C)  7.08 feet 
D)  12.32 feet 
E)  5.87 feet

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

A) 390,625 
B) 78,125 
C) 1,000,000 
D) 1,953,125 
E)  3,125 
A) 390,625 
B) 78,125 
C) 1,000,000 
D) 1,953,125 
E)  3,125

Question 17

Find the standard form of the complex number shown below.

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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)  a= 8.37 
B)  a= 10.02 
C)  a= 5.92 
D)  a= 21.05 
E)  a= 7.14 
A)  a= 8.37 
B)  a= 10.02 
C)  a= 5.92 
D)  a= 21.05 
E)  a= 7.14

Question 20

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

Accepted Answer

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

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

Find the trigonometric form of .

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

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

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

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

Find the trigonometric form of .

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

A 725-pound trailer is sitting on an exit ramp inclined at 36° on Highway 35. How much force is required to keep the trailer from rolling back down the exit ramp? Round answer to two decimal places.

final If and , and the vectors make angles of 0° and 60° and with the x-axis respectively, find the component form of the sum of u and v. Round answers to two decimal places.

Find the projection of u onto v if , .

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

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.

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

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

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

Find the standard form of the complex number shown below.

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

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

Divide the complex numbers below and leave the result in trigonometric 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

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

Find the trigonometric form of .

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

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

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

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

Find the trigonometric form of .

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

A 725-pound trailer is sitting on an exit ramp inclined at 36° on Highway 35. How much force is required to keep the trailer from rolling back down the exit ramp? Round answer to two decimal places.

final If and , and the vectors make angles of 0° and 60° and with the x-axis respectively, find the component form of the sum of u and v. Round answers to two decimal places.

Find the projection of u onto v if , .

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

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.

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

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

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

Find the standard form of the complex number shown below.

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

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

Divide the complex numbers below and leave the result in trigonometric 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