Question 1

Solve

Accepted Answer

A)    
B)    
C)    
D)    
E) No triangle exists 
A)    
B)    
C)    
D)    
E) No triangle exists

Question 2

Given that   , find the number.

Accepted Answer

A) 14 
B) 7 
C) -9 
D) 49 
E) 33 
A) 14 
B) 7 
C) -9 
D) 49 
E) 33

Question 3

A triangular field has sides of lengths a, b, and c (in yards). Approximate the number of acres in the field (   ).

Accepted Answer

A) 10.67 acres 
B) 11.00 acres 
C) 11.28 acres 
D) 3.27 acres 
E) 9.47 acres 
A) 10.67 acres 
B) 11.00 acres 
C) 11.28 acres 
D) 3.27 acres 
E) 9.47 acres

Question 4

Find || a ||. a = -

Accepted Answer

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

Question 5

A helicopter hovers at an altitude that is   feet above a mountain peak of altitude 5,122 feet, as shown in the figure. A second, taller peak is viewed from both the mountaintop and the helicopter. From the helicopter, the angle of depression is   , and from the mountaintop, the angle of elevation is   .   Approximate the altitude of the taller peak.

Accepted Answer

A) 5,429 ft 
B) 5,431 ft 
C) 5,427 ft 
D) 4,817 ft 
E) 5,421 ft 
A) 5,429 ft 
B) 5,431 ft 
C) 5,427 ft 
D) 4,817 ft 
E) 5,421 ft

Question 6

Use De Moivre's theorem to change the given complex number to the form   , where   and   are real numbers.

Accepted Answer

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

Question 7

Find the two square roots of

Accepted Answer

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

Question 8

Express in the form   , where a and b are real numbers.

Accepted Answer

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

Question 9

Find (a) the dot product of the two vectors and (b) the angle between the two vectors.   and

Accepted Answer

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

Question 10

The trigonometric form of complex numbers is often used by electrical engineers to describe the current I, voltage V, and impedance Z in electrical circuits with alternating current. Impedance is the opposition to the flow of current in a circuit. Most common electrical devices operate on 115-volt, alternating current. The relationship among these three quantities is   . The real part of I represents the actual current delivered to an electrical appliance in amps. Approximate this current when   and   , and express the answer in rectangular form to two decimal places.

Accepted Answer

A) 2.61 amps 
B) 1.30 amps 
C) 1.37 amps 
D) 1.25 amps 
E) 1.15 amps 
A) 2.61 amps 
B) 1.30 amps 
C) 1.37 amps 
D) 1.25 amps 
E) 1.15 amps

Question 11

Represent the complex number geometrically.

Accepted Answer

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

Question 12

Use De Moivre's theorem to change the given complex number to the form   , where   and   are real numbers.

Accepted Answer

A) 4,096 
B) -24+24i 
C) 2,048 
D) -4,096i 
E) -2,048i 
A) 4,096 
B) -24+24i 
C) 2,048 
D) -4,096i 
E) -2,048i

Question 13

Find (a) the dot product of the two vectors and (b) the angle between the two vectors.   and

Accepted Answer

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

Question 14

Find (a) the dot product of the two vectors and (b) the angle between the two vectors.   and

Accepted Answer

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

Question 15

Represent the complex number geometrically.

Accepted Answer

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

Question 16

Find 2a + 5b. a = , b =

Accepted Answer

A) 2a + 5b =  
B) 2a + 5b =  
C) 2a + 5b =  
D) 2a + 5b =  
E) 2a + 5b =  
A) 2a + 5b =  
B) 2a + 5b =  
C) 2a + 5b =  
D) 2a + 5b =  
E) 2a + 5b =

Question 17

Find 5a - 2b. a = i + 4j, b = 6i - 6j

Accepted Answer

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

Question 18

Given that   , find the number.

Accepted Answer

A) 13 
B) 10 
C) -7 
D) 25 
E) 5 
A) 13 
B) 10 
C) -7 
D) 25 
E) 5

Question 19

Find the absolute value.

Accepted Answer

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

Question 20

A triangular field has sides of lengths a, b, and c (in yards). Approximate the number of acres in the field (   ).

Accepted Answer

A) 9.80 acres 
B) 10.13 acres 
C) 10.41 acres 
D) 3.13 acres 
E) 11.00 acres 
A) 9.80 acres 
B) 10.13 acres 
C) 10.41 acres 
D) 3.13 acres 
E) 11.00 acres

Solve

Given that , find the number.

A triangular field has sides of lengths a, b, and c (in yards). Approximate the number of acres in the field ( ).

Find || a ||. a = - < 7, - 5 >

Use De Moivre's theorem to change the given complex number to the form , where and are real numbers.

Find the two square roots of

Express in the form , where a and b are real numbers.

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Represent the complex number geometrically.

Use De Moivre's theorem to change the given complex number to the form , where and are real numbers.

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Represent the complex number geometrically.

Find 2a + 5b. a = < 2, - 2>, b = <6, 2 >

Find 5a - 2b. a = i + 4j, b = 6i - 6j

Given that , find the number.

Find the absolute value.

A triangular field has sides of lengths a, b, and c (in yards). Approximate the number of acres in the field ( ).

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

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Exam 8: Applications of Trigonometry

Solve

Given that , find the number.

A triangular field has sides of lengths a, b, and c (in yards). Approximate the number of acres in the field ( ).

Find || a ||. a = - < 7, - 5 >

Use De Moivre's theorem to change the given complex number to the form , where and are real numbers.

Find the two square roots of

Express in the form , where a and b are real numbers.

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Represent the complex number geometrically.

Use De Moivre's theorem to change the given complex number to the form , where and are real numbers.

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. and

Represent the complex number geometrically.

Find 2a + 5b. a = < 2, - 2>, b = <6, 2 >

Find 5a - 2b. a = i + 4j, b = 6i - 6j

Given that , find the number.

Find the absolute value.

A triangular field has sides of lengths a, b, and c (in yards). Approximate the number of acres in the field ( ).

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

Filters