Trigonometry for Engineering Technology is designed to teach the fundamentals to students new to the subject and is also useful for in-house training programs and as a self-study refresher. The text uses mechanical, civil, and architectural applications to enhance its explanations of real-world scenarios. Its open format enables it to be used as a workbook either in class or for independent study.  In addition to its thorough treatment of right-angle trigonometry, the text includes oblique triangle calculations and graphing of trigonometric functions.  The examples in each chapter demonstrate a specific type of problem-solving procedure and are followed by practice exercises. Answers and complete solutions to the exercises are included in the appendix.
 

 Gary Powers has taught a wide range of classes for more than 15 years at South Hills School of Business and Technology, a two-year, post-secondary school located in State College, PA., including Geometry, Trigonometry, Physics, Dimensional Metrology, Machining, CNC Programming, and Mechanical Design. His students regularly serve internships with and are hired by a variety of engineering and manufacturing firms. Previously, Gary was employed for 16 years by Corning, Inc. as a manufacturing supervisor and process engineer. He holds a B.S. in Aerospace Engineering from the U.S. Naval Academy, and after graduating from the Naval Nuclear Power School he served in the submarine force. Gary is a member of the American Society of Engineering Education.  

 Contents

 

Chapter 1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

 

Why Is Trigonometry Important?

1

 

Types of Trigonometry

1

 

Examples of Applications

2

 

 

 

Chapter 2

Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

 

Introduction

5

 

What Is an Angle?

5

 

Angular Units

6

 

Formats for Expressing Degrees

7

 

Naming Angles

8

 

Measuring Angles

10

 

Using Your Calculator

12

 

Entering and Converting Degrees with the TI-30XA

13

 

Entering and Converting Degrees with the TI-30XIIS

14

 

Adding and Subtracting Angles

17

 

 

 

Chapter 3

Triangles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

 

Right Triangles

21

 

Other Types of Triangles

22

 

The Sum of Interior Angles

23

 

Pythagorean Theorem

26

 

 

 

Chapter 4

Preparation for Right Angle Trigonometry . . . . . . . . . .

31

 

Similar Triangles

31

 

Corresponding Sides

32

 

Proportional Sides

35

 

Naming Sides in a Right Triangle

39

 

Chapters 2–4, Practice Worksheet . . . . . . . . . . . . . . . . .

41

 

 

 

Chapter 5

Functions of Trigonometry . . . . . . . . . . . . . . . . . . . . . . .

47

 

Sine Function

47

 

Cosine Funtion

48

 

Tangent Function

51

 

Function Practice

53

 

Summary of Trigonometry Functions

55

 

Other Trigonometric Functions

55

 

 

 

Chapter 6

Solving for Unknown Sides . . . . . . . . . . . . . . . . . . . . . . .

57

b

Introduction

57

 

Solving for an Unknown Side

58

 

Create an Equation to Solve for an Unknown Side

59

 

Solving for an Unknown Side

61

 

Trigonometry Functions in Your Calculator

62

 

Positive and Negataive Trigonometry Values

63

 

Alternate Solution to Solving for an Unknown Side

65

 

Cofunctions

66

 

Complete the Solution

67

 

Practice in Solving for Unknown Sides

68

 

 

 

Chapter 7

Solving for Unknown Angles . . . . . . . . . . . . . . . . . . . . . .

73

 

Introduction

73

 

Solving for an Unknown Angle

74

 

Create an Equation to Solve for an Unknown Angle

75

 

Inverse Trigonometry Functions in Your Calculator

77

 

How to Avoid Rounding an Intermediate Calculation

78

 

Errors Caused by Intermediate Rounding

78

 

Complete the Solution

79

 

Problem Solving Steps

80

 

Naming Conventions for Inverse Functions

80

 

Practice in Solving for Unknown Angles

81

 

Chapter 6-7, Practice Worksheet

85

 

 

 

Chapter 8

Mechanical Applications . . . . . . . . . . . . . . . . . . . . . . . . .

89

 

Mechanical Technology Applications

89

 

Drill Point Depth

90

 

Angularity Measurement with a Sine Bar

92

 

Drill Depth for Engraving

95

 

Identify X and Y Locations on a Part

97

 

Hole Locations on a Bolt-Hole Circle

99

 

V-Block Inspection

102

 

Dovetail Slide Inspection

105

 

Tapers

107

 

Practice Worksheet

109

 

 

 

Chapter 9

Civil Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

113

 

Civil Technology Applications

113

 

Horizontal Distance and Slope Angle

114

 

The Height of a Structure

117

 

Distance across an Obstruction

119

 

Northing and Easting of a Survey Point

122

 

Bearing Format for Directions

126

 

Slope Angle and Grade

128

 

Contour Lines

129

 

Practice Worksheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

132

 

 

 

Chapter 10

Architectural and Construction Applications . . . . . . . .

137

 

Architectural and Construction Applications

137

 

Roof Pitch

138

 

Roof Truss Dimensions

140

 

3-4-5 Triangles

144

 

Stair Dimensions

147

 

Practice Worksheet for Chapter 10 . . . . . . . . . . . . . . . . . . .

150

 

 

 

Chapter 11

Graphing Trigonometry Functions. . . . . . . . . . . . . . . . .

157

 

Mechanical Waves

158

 

Radian Units

165

 

Rotational Motion

166

 

Sound Waves

169

 

Alternating Current

171

 

Graph of Cosine Function

174

 

 

 

Chapter 12

Law of Sines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

177

 

Law of Sines Formula

177

 

Problem Solving with Law of Sines

178

 

Civil Application

181

 

Architectural Application

184

 

 

 

Chapter 13

Law of Cosines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

187

 

Law of Cosines Formula

187

 

Special Case of the Law of Cosines

188