Question 1

Find the angle between the vectors u and v.

Accepted Answer

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

Question 2

Given that   and   , find the angle beween the forces if the magnitude of the resultant force is   . Round answer to the nearest degree.

Accepted Answer

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

Question 3

Determine a value for b such that a triangle with   and   has only one solution.

Accepted Answer

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

Question 4

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

Question 5

A vertical pole 37 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 61 feet downhill from the base of the pole. Round answer to two decimal places.

Accepted Answer

A)    feet 
B) 84.88 feet 
C) 70.73 feet 
D) 75.45 feet 
E) 61.40 feet 
A)    feet 
B) 84.88 feet 
C) 70.73 feet 
D) 75.45 feet 
E) 61.40 feet

Question 6

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

Accepted Answer

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

Question 7

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 8

If   and   , find   .

Accepted Answer

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

Question 9

Determine a value for b such that a triangle with   and   has two solutions.

Accepted Answer

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

Question 10

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

Question 11

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 12

Find a unit vector in the direction of   .

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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 15

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]

Accepted Answer

A)    
B)    
C)    
D)    
E) none of these 
A)    
B)    
C)    
D)    
E) none of these

Question 16

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 17

Represent the complex number below graphically.

Accepted Answer

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

Question 18

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

Question 19

A triangular parcel of land has sides of lengths   feet. Approximate the area of the land. Round answer to nearest foot.

Accepted Answer

A) 230,678 ft2 
B) 230,010 ft2 
C) 229,462 ft2 
D) 229,402 ft2 
E) 229,950 ft2 
A) 230,678 ft2 
B) 230,010 ft2 
C) 229,462 ft2 
D) 229,402 ft2 
E) 229,950 ft2

Question 20

Given   and   , determine   .

Accepted Answer

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

Find the angle between the vectors u and v.

Given that and , find the angle beween the forces if the magnitude of the resultant force is . Round answer to the nearest degree.

Determine a value for b such that a triangle with and has only one solution.

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

A vertical pole 37 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 61 feet downhill from the base of the pole. Round answer to two decimal places.

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

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

If and , find .

Determine a value for b such that a triangle with and has two solutions.

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

Find a unit vector in the direction of .

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

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

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]

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

Represent the complex number below graphically.

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

A triangular parcel of land has sides of lengths feet. Approximate the area of the land. Round answer to nearest foot.

Given and , determine .

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 angle between the vectors u and v.

Given that and , find the angle beween the forces if the magnitude of the resultant force is . Round answer to the nearest degree.

Determine a value for b such that a triangle with and has only one solution.

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

A vertical pole 37 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 61 feet downhill from the base of the pole. Round answer to two decimal places.

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

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

If and , find .

Determine a value for b such that a triangle with and has two solutions.

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

Find a unit vector in the direction of .

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

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

Using the figure below, sketch a graph of the given vector. [The graphs in the answer choices are drawn to the same scale as the graph below.]

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

Represent the complex number below graphically.

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

A triangular parcel of land has sides of lengths feet. Approximate the area of the land. Round answer to nearest foot.

Given and , determine .

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