Question 1

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 2

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

Accepted Answer

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

Question 3

Find the component form of vector v.

Accepted Answer

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

Question 4

Graphically represent the following complex number.

Accepted Answer

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

Question 5

Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of   at 11 miles per hour, and the other travels at a bearing of   at 13 miles per hour. Approximate the distance between them at noon the same day. Round answer to two decimal places.

Accepted Answer

A) 16.85 miles 
B) 33.51 miles 
C) 22.38 miles 
D) 18.89 miles 
E) 29.39 miles 
A) 16.85 miles 
B) 33.51 miles 
C) 22.38 miles 
D) 18.89 miles 
E) 29.39 miles

Question 6

Given   ,   , and   , 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 7

Find the magnitude and direction angle of   . Round direction angle to nearest degree.

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Given   ,   , and   , use Heron's Area Formula to find the area of triangle   . Round 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 10

Find the magnitude of vector v.

Accepted Answer

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

Question 11

Given   and   , determine   .

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Find a unit vector in the direction of   .

Accepted Answer

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

Question 15

Use vectors to find the measure of the angle at vertex B of triangle ABC, when   . Round answer to two decimal places.

Accepted Answer

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

Question 16

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 17

Find the absolute value of the complex number   .

Accepted Answer

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

Question 18

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 19

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

Question 20

Find the trigonometric form of the complex number shown below.

Accepted Answer

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

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 B. Round answer to two decimal places.

Find the component form of vector v.

Graphically represent the following complex number.

Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of at 11 miles per hour, and the other travels at a bearing of at 13 miles per hour. Approximate the distance between them at noon the same day. Round answer to two decimal places.

Given , , and , 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.

Find the magnitude and direction angle of . Round direction angle to nearest degree.

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

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

Find the magnitude of vector v.

Given and , determine .

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

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

Find a unit vector in the direction of .

Use vectors to find the measure of the angle at vertex B of triangle ABC, when . 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.

Find the absolute value of the complex number .

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

Find the trigonometric form of the complex number shown 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 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 B. Round answer to two decimal places.

Find the component form of vector v.

Graphically represent the following complex number.

Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of at 11 miles per hour, and the other travels at a bearing of at 13 miles per hour. Approximate the distance between them at noon the same day. Round answer to two decimal places.

Given , , and , 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.

Find the magnitude and direction angle of . Round direction angle to nearest degree.

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

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

Find the magnitude of vector v.

Given and , determine .

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

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

Find a unit vector in the direction of .

Use vectors to find the measure of the angle at vertex B of triangle ABC, when . 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.

Find the absolute value of the complex number .

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

Find the trigonometric form of the complex number shown 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