Question 1

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 2

In the figure below,   ,   , and   . Use this information to solve the parallelogram for F$\beta$. 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 3

Find the fourth roots of   Write the roots in trigonometric form.

Accepted Answer

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

Question 4

Find the absolute value of the complex number   .

Accepted Answer

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

Question 5

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 6

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)  10.20 feet 
B)  3.30 feet 
C)  6.27 feet 
D)  6.63 feet 
E)  12.32 feet 
A)  10.20 feet 
B)  3.30 feet 
C)  6.27 feet 
D)  6.63 feet 
E)  12.32 feet

Question 7

Write the complex number shown below in trigonometric form.

Accepted Answer

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

Question 8

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)    
C)    
D)    
E)  not possible 
A)    
B)    
C)    
D)    
E)  not possible

Question 9

Given   and   , determine   .

Accepted Answer

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

Question 10

Find the angle between the vectors u and v.

Accepted Answer

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

Question 11

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)  9.25 
B)  13.55 
C)  17.84 
D)  10.33 
E)  11.40 
A)  9.25 
B)  13.55 
C)  17.84 
D)  10.33 
E)  11.40

Question 12

Given   and   , determine   .

Accepted Answer

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

Question 13

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 14

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 15

Use the dot product to find the magnitude of u if

Accepted Answer

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

Question 16

Find the trigonometric form of the complex number represented graphically.

Accepted Answer

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

Question 17

Given that Force 1 = 70 pounds and Force 2 = 120 pounds, find the angle between the forces if the magnitude of the resultant force is 90 pounds. Round answer to the nearest degree.

Accepted Answer

A)  60° 
B)  40° 
C)  53° 
D)  45° 
E)  48° 
A)  60° 
B)  40° 
C)  53° 
D)  45° 
E)  48°

Question 18

Find the absolute value of the complex number   .

Accepted Answer

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

Question 19

Find the trigonometric form of the complex number represented graphically.

Accepted Answer

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

Question 20

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

Accepted Answer

A)  43.69 sq. units 
B)  49.15 sq. units 
C)  54.61 sq. units 
D)  65.53 sq. units 
E)  60.07 sq. units 
A)  43.69 sq. units 
B)  49.15 sq. units 
C)  54.61 sq. units 
D)  65.53 sq. units 
E)  60.07 sq. units

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

Find the fourth roots of Write the roots in trigonometric form.

Find the absolute value of the complex number .

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

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.

Write the complex number shown below 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.

Given and , determine .

Find the angle between the vectors u and v.

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

Given and , determine .

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

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

Use the dot product to find the magnitude of u if

Find the trigonometric form of the complex number represented graphically.

Given that Force 1 = 70 pounds and Force 2 = 120 pounds, find the angle between the forces if the magnitude of the resultant force is 90 pounds. Round answer to the nearest degree.

Find the absolute value of the complex number .

Find the trigonometric form of the complex number represented graphically.

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

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Exam 7: Additional Topics in Trigonometry

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

In the figure below, , , and . Use this information to solve the parallelogram for F β\betaβ . The diagonals of the parallelogram are represented by c and d. Round answer to two decimal places.

Find the fourth roots of Write the roots in trigonometric form.

Find the absolute value of the complex number .

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

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.

Write the complex number shown below 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.

Given and , determine .

Find the angle between the vectors u and v.

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

Given and , determine .

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

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

Use the dot product to find the magnitude of u if

Find the trigonometric form of the complex number represented graphically.

Given that Force 1 = 70 pounds and Force 2 = 120 pounds, find the angle between the forces if the magnitude of the resultant force is 90 pounds. Round answer to the nearest degree.

Find the absolute value of the complex number .

Find the trigonometric form of the complex number represented graphically.

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