Question 1

Given that   , find the number.

Accepted Answer

A) 40 
B) 64 
C) -112 
D) -56 
E) -60 
A) 40 
B) 64 
C) -112 
D) -56 
E) -60

Question 2

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 3

Determine m such that the two vectors are orthogonal.   and

Accepted Answer

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

Question 4

Find 4a + 3b. a = , b =

Accepted Answer

A) 4a + 3b =  
B) 4a + 3b =  
C) 4a + 3b =  
D) 4a + 3b =  
E) 4a + 3b =  
A) 4a + 3b =  
B) 4a + 3b =  
C) 4a + 3b =  
D) 4a + 3b =  
E) 4a + 3b =

Question 5

Shown in the figure is a plan for the top of a wing of a jet fighter, where   feet and   feet.   Approximate the area of triangle ABC.

Accepted Answer

A) 442.7 ft 2  
B) 442.1 ft 2  
C) 885.0 ft 2  
D) 443.1 ft 2  
E) 442.5 ft 2  
A) 442.7 ft 2  
B) 442.1 ft 2  
C) 885.0 ft 2  
D) 443.1 ft 2  
E) 442.5 ft 2

Question 6

Express the complex number in trigonometric form with   .

Accepted Answer

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

Question 7

Determine m such that the two vectors are orthogonal.   and

Accepted Answer

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

Question 8

The volume V of the right triangular prism shown in the figure is   where B is the area of the base and h is the height of the prism.   Approximate h, if   .

Accepted Answer

A) 5.6 
B) 19.5 
C) 20.7 
D) 19.9 
E) 21.1 
A) 5.6 
B) 19.5 
C) 20.7 
D) 19.9 
E) 21.1

Question 9

A cathedral is located on a hill, as shown in the figure. When the top of the spire is viewed from the base of the hill, the angle of elevation is   . When it is viewed at a distance of   feet from the base of the hill, the angle of elevation is   . The hill rises at an angle of   .   Approximate the height of the cathedral.

Accepted Answer

A) 737 ft 
B) 735 ft 
C) 1,610 ft 
D) 739 ft 
E) 733 ft 
A) 737 ft 
B) 735 ft 
C) 1,610 ft 
D) 739 ft 
E) 733 ft

Question 10

If c represents a constant force, find the work done if the point of application of c moves along the line segment from P to Q.   and

Accepted Answer

A) 48 
B) 12 
C) -24 
D) -12 
E) 21 
A) 48 
B) 12 
C) -24 
D) -12 
E) 21

Question 11

Find the two square roots of

Accepted Answer

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

Question 12

Approximate the area of a parallelogram that has sides of lengths a and b (in feet) if one angle at a vertex has measure   .

Accepted Answer

A) 110.5 
B) 116.4 
C) 134.8 
D) 117.3 
E) 113.1 
A) 110.5 
B) 116.4 
C) 134.8 
D) 117.3 
E) 113.1

Question 13

Find 4a + 6b. a = , b =

Accepted Answer

A) 4a + 6b =  
B) 4a + 6b =  
C) 4a + 6b =  
D) 4a + 6b =  
E) 4a + 6b =  
A) 4a + 6b =  
B) 4a + 6b =  
C) 4a + 6b =  
D) 4a + 6b =  
E) 4a + 6b =

Question 14

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 15

Represent the complex number geometrically.

Accepted Answer

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

Question 16

Determine whether the given pair of vectors are orthogonal or not.   and

Accepted Answer

A) no 
B) yes 
A) no 
B) yes

Question 17

If forces F 1 , F 2 ,..., F n  act at a point P, the net (or resultant) force F is the sum   If   the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F.
B ) Find an additional force G such that equilibrium occurs.

Accepted Answer

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

Question 18

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 19

Shown in the figure is a plan for the top of a wing of a jet fighter, where   feet and   feet.   Approximate angle   .

Accepted Answer

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

Question 20

Find 2a - 3b. a = i + 2j, b = 3i - 5j

Accepted Answer

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

Given that , find the number.

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

Determine m such that the two vectors are orthogonal. and

Find 4a + 3b. a = < 4, - 2>, b = <4, 5 >

Shown in the figure is a plan for the top of a wing of a jet fighter, where feet and feet. Approximate the area of triangle ABC.

Express the complex number in trigonometric form with .

Determine m such that the two vectors are orthogonal. and

The volume V of the right triangular prism shown in the figure is where B is the area of the base and h is the height of the prism. Approximate h, if .

If c represents a constant force, find the work done if the point of application of c moves along the line segment from P to Q. and

Find the two square roots of

Approximate the area of a parallelogram that has sides of lengths a and b (in feet) if one angle at a vertex has measure .

Find 4a + 6b. a = < 5, - 4>, b = <6, 5 >

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

Represent the complex number geometrically.

Determine whether the given pair of vectors are orthogonal or not. and

If forces F₁, F₂,..., F_n act at a point P, the net (or resultant) force F is the sum If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F. B ) Find an additional force G such that equilibrium occurs.

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

Shown in the figure is a plan for the top of a wing of a jet fighter, where feet and feet. Approximate angle .

Find 2a - 3b. a = i + 2j, b = 3i - 5j

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

Exam 8: Applications of Trigonometry

Given that , find the number.

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

Determine m such that the two vectors are orthogonal. and

Find 4a + 3b. a = < 4, - 2>, b = <4, 5 >

Shown in the figure is a plan for the top of a wing of a jet fighter, where feet and feet. Approximate the area of triangle ABC.

Express the complex number in trigonometric form with .

Determine m such that the two vectors are orthogonal. and

The volume V of the right triangular prism shown in the figure is where B is the area of the base and h is the height of the prism. Approximate h, if .

If c represents a constant force, find the work done if the point of application of c moves along the line segment from P to Q. and

Find the two square roots of

Approximate the area of a parallelogram that has sides of lengths a and b (in feet) if one angle at a vertex has measure .

Find 4a + 6b. a = < 5, - 4>, b = <6, 5 >

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

Represent the complex number geometrically.

Determine whether the given pair of vectors are orthogonal or not. and

If forces F 1 , F 2 ,..., F n act at a point P, the net (or resultant) force F is the sum If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F. B ) Find an additional force G such that equilibrium occurs.

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

Shown in the figure is a plan for the top of a wing of a jet fighter, where feet and feet. Approximate angle .

Find 2a - 3b. a = i + 2j, b = 3i - 5j

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

If forces F₁, F₂,..., F_n act at a point P, the net (or resultant) force F is the sum If the forces are said to be in equilibrium. The given forces act at the origin O of an xy-plane. a) Find the net force F. B ) Find an additional force G such that equilibrium occurs.