Question 1

Find the trigonometric form of the complex number shown below.

Accepted Answer

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

Question 2

Find the standard form of the complex number shown below.

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 following complex number.

Accepted Answer

A) 19,683 
B) 6,561 
C) 2,187 
D) 46,656 
E) 243 
A) 19,683 
B) 6,561 
C) 2,187 
D) 46,656 
E) 243

Question 4

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

Accepted Answer

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

Question 5

Determine the area of a triangle having the following measurements. Round your 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 6

Use the dot product to find the magnitude of u if   .

Accepted Answer

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

Question 7

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 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   if   , and   , where   is the angle between u and v. Round answer to two decimal places.

Accepted Answer

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

Question 10

Determine a value for b such that a triangle with   and   has no solution. Round your answer to the nearest hundredth.

Accepted Answer

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

Question 11

Find all solutions to the following equation.

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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 14

Perform the operation shown below and leave the result in trigonometric form.

Accepted Answer

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

Question 15

Perform the operation shown below and leave the result in trigonometric form.

Accepted Answer

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

Question 16

Three forces with magnitudes of   pounds,   pounds, and   pounds act on an object at angles   ,   , and   , respectively, with the positive x-axis. Find the magnitude and direction of the resultant force. Round answers to two decimal places.

Accepted Answer

A)    pounds;   
B) 130.55 pounds;   
C)    pounds;   
D)    pounds;   
E) 130.55 pounds;   
A)    pounds;   
B) 130.55 pounds;   
C)    pounds;   
D)    pounds;   
E) 130.55 pounds;

Question 17

Find the trigonometric form of the complex number shown below.

Accepted Answer

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

Question 18

Find the magnitude and direction angle of   .

Accepted Answer

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

Question 19

A   -pound trailer is sitting on an exit ramp inclined at   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)    pounds 
B)    pounds 
C)    pounds 
D)    pounds 
E)    pounds 
A)    pounds 
B)    pounds 
C)    pounds 
D)    pounds 
E)    pounds

Question 20

Given vectors   and   , determine the quantity indicated below.

Accepted Answer

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

Find the trigonometric form of the complex number shown below.

Find the standard form of the complex number shown below.

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

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

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

Use the dot product to find the magnitude of u if .

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

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

Determine if , and , where is the angle between u and v. Round answer to two decimal places.

Determine a value for b such that a triangle with and has no solution. Round your answer to the nearest hundredth.

Find all solutions to the following equation.

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 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 A. Round answer to two decimal places.

Perform the operation shown below and leave the result in trigonometric form.

Perform the operation shown below and leave the result in trigonometric form.

Three forces with magnitudes of pounds, pounds, and pounds act on an object at angles , , and , respectively, with the positive x-axis. Find the magnitude and direction of the resultant force. Round answers to two decimal places.

Find the trigonometric form of the complex number shown below.

Find the magnitude and direction angle of .

A -pound trailer is sitting on an exit ramp inclined at 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.

Given vectors and , determine the quantity indicated below.

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

Find the trigonometric form of the complex number shown below.

Find the standard form of the complex number shown below.

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

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

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

Use the dot product to find the magnitude of u if .

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

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

Determine if , and , where is the angle between u and v. Round answer to two decimal places.

Determine a value for b such that a triangle with and has no solution. Round your answer to the nearest hundredth.

Find all solutions to the following equation.

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 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 A. Round answer to two decimal places.

Perform the operation shown below and leave the result in trigonometric form.

Perform the operation shown below and leave the result in trigonometric form.

Three forces with magnitudes of pounds, pounds, and pounds act on an object at angles , , and , respectively, with the positive x-axis. Find the magnitude and direction of the resultant force. Round answers to two decimal places.

Find the trigonometric form of the complex number shown below.

Find the magnitude and direction angle of .

A -pound trailer is sitting on an exit ramp inclined at 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.

Given vectors and , determine the quantity indicated below.

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