Technical Mathematics

by Smith,Robert D.

• ISBN13: 9780766828018
• ISBN10: 0766828018
• Format: Paperback
• Copyright: 2001-10-12
• Publisher: Cengage Learning

Summary

Available in both hard- and soft-cover editions, Technical Mathematics underscores the importance of algebra, geometry, and trigonometry in today's sophisticated, state-of-the-art trade/technical work environments. Unlike other books, this book integrates practice problems and examples directly into its explanations of math concepts and eliminates the need to labor through theoretical derivations and formal proofs. In addition to new, step-by-step examples and applications problems drawn directly from a variety of diverse occupational fields, this edition also features expanded coverage of fractional exponents, measurement prefixes used in the electronics and computer industries, the binary system, polar coordinates, quadratic equations, and more! Integration of algebraic and geometric principles with trigonometry, combined with thoughtful sequencing of the material, helps readers develop the analytic and critical thinking skills required to solve realistic, occupation-specific problems. Available in both hard- and soft-cover editions, Technical Mathematics underscores the importance of algebra, geometry, and trigonometry in today's sophisticated, state-of-the-art trade/technical work environments. It integrates practice problems and examples directly into its explanations of math concepts and eliminates the need to labor through theoretical derivations and formal proofs. With new, step-by-step examples and applications problems drawn directly from a variety of diverse occupational fields, this edition also features expanded coverage of fractional exponents, measurement prefixes used in the electronics and computer industries, the binary system, polar coordinates, quadratic equations, and more!

Author Biography

Robert D. Smith is an Associate Professor Emeritus of Industrial Technology at Central Connecticut State University in New Britain, Connecticut

Table of Contents

Preface	xv
SECTION I Fundamentals of General Mathematics	1	(164)
Whole Numbers	2	(29)
Place Value	2	(1)
Expanding Whole Numbers	3	(1)
Estimating (Approximating)	4	(1)
Addition of Whole Numbers	5	(1)
Subtraction of Whole Numbers	6	(2)
Problem Solving-Word Problem Practical Applications	8	(1)
Adding and Subtracting Whole Numbers in Practical Applications	8	(2)
Multiplication of Whole Numbers	10	(3)
Division of Whole Numbers	13	(3)
Multiplying and Dividing Whole Numbers in Practical Applications	16	(3)
Combined Operations of Whole Numbers	19	(1)
Combined Operations of Whole Numbers in Practical Applications	20	(7)
Unit Exercise and Problem Review	23	(4)
Computing with a Calculator: Whole Numbers	27	(4)
Common Fractions	31	(46)
Definitions	31	(1)
Fractional Parts	32	(1)
A Fraction as an Indicated Division	33	(1)
Equivalent Fractions	33	(1)
Expressing Fractions in Lowest Terms	33	(1)
Expressing Mixed Numbers as Improper Fractions	34	(1)
Expressing Improper Fractions as Mixed Numbers	35	(1)
Use of Common Fractions in Practical Applications	36	(2)
Addition of Common Fractions	38	(4)
Subtraction of Common Fractions	42	(3)
Adding and Subtracting Common Fractions in Practical Applications	45	(4)
Multiplication of Common Fractions	49	(4)
Multiplying Common Fractions in Practical Applications	53	(3)
Division of Common Fractions	56	(3)
Dividing Common Fractions in Practical Applications	59	(2)
Combined Operations With Common Fractions	61	(2)
Combined Operations of Common Fractions in Practical Applications	63	(8)
Unit Exercise and Problem Review	66	(5)
Computing with a Calculator: Fractions and Mixed Numbers	71	(6)
Decimal Fractions	77	(48)
Meaning of Fractional Parts	78	(1)
Reading Decimal Fractions	78	(1)
Simplified Method of Reading Decimal Fractions	79	(1)
Writing Decimal Fractions	79	(1)
Rounding Decimal Fractions	80	(1)
Expressing Common Fractions as Decimal Fractions	80	(1)
Expressing Decimal Fractions as Common Fractions	81	(1)
Decimal Fractions in Practical Applications	82	(1)
Adding Decimal Fractions	83	(1)
Subtracting Decimal Fractions	84	(1)
Adding and Subtracting Decimal Fractions in Practical Applications	85	(3)
Multiplying Decimal Fractions	88	(2)
Multiplying Decimal Fractions in Practical Applications	90	(3)
Dividing Decimal Fractions	93	(2)
Dividing Decimal Fractions in Practical Applications	95	(3)
Powers and Roots of Decimal Fractions	98	(3)
Decimal Fraction Powers and Roots in Practical Applications	101	(4)
Table of Decimal Equivalents	105	(2)
Combined Operations of Decimal Fractions	107	(2)
Combined Operations of Decimal Fractions in Practical Applications	109	(10)
Unit Exercise and Problem Review	112	(7)
Computing with a Calculator: Decimals	119	(6)
Percents	125	(16)
Definition of Percent	125	(1)
Expressing Decimal Fractions as Percents	126	(1)
Expressing Common Fractions and Mixed Numbers as Percents	126	(1)
Expressing Percents as Decimal Fractions	127	(1)
Expressing Percents as Common Fractions	128	(1)
Types of Simple Percentage Problems	128	(2)
Finding Percentage in Practical Applications	130	(2)
Finding Percent (Rate) in Practical Applications	132	(2)
Finding the Base in Practical Applications	134	(1)
More Complex Percentage Practical Applications	135	(6)
Unit Exercise and Problem Review	138	(3)
Graphs: Bar and Line	141	(24)
Types and Structure of Graphs	141	(1)
Reading Bar Graphs	142	(4)
Drawing Bar Graphs	146	(2)
Line Graphs	148	(1)
Reading Line Graphs	149	(1)
Reading Combined-Data Line Graphs	150	(5)
Drawing Line Graphs	155	(1)
Drawing Broken-Line Graphs	155	(2)
Drawing Straight-Line Graphs	157	(1)
Drawing Curved-Line Graphs	158	(7)
Unit Exercise and Problem Review	160	(5)
SECTION II Measurement	165	(82)
Precision, Accuracy, and Tolerance	166	(16)
Exact and Approximate (Measurement) Numbers	166	(1)
Degree of Precision of Measuring Instruments	167	(1)
Common Linear Measuring Instruments	167	(1)
Degree of Precision of a Measurement Number	168	(1)
Degrees of Precision in Adding and Subtracting Measurement Numbers	169	(1)
Significant Digits	170	(1)
Accuracy	171	(1)
Accuracy in Multiplying and Dividing Measurement Numbers	171	(1)
Absolute and Relative Error	172	(1)
Tolerance (Linear)	173	(1)
Unilateral and Bilateral Tolerance with Clearance and Interference Fits	174	(8)
Unit Exercise and Problem Review	177	(5)
Measurement Units	182	(40)
Customary Linear Units	183	(1)
Expressing Equivalent Units of Measure	183	(3)
Arithmetic Operations with Compound Numbers	186	(4)
Customary Linear Measure Practical Applications	190	(3)
Metric Units of Linear Measure	193	(1)
Expressing Equivalent Units within the Metric System	194	(2)
Arithmetic Operations with Metric Lengths	196	(1)
Metric Linear Measure Practical Applications	196	(2)
Customary Units of Surface Measure (Area)	198	(1)
Customary Area Measure Practical Applications	199	(1)
Metric Units of Surface Measure (Area)	200	(2)
Arithmetic Operations with Metric Area Units	202	(1)
Metric Area Measure Practical Applications	202	(1)
Customary Units of Volume (Cubic Measure)	203	(1)
Customary Volume Practical Applications	204	(1)
Metric Units of Volume (Cubic Measure)	205	(2)
Arithmetic Operations with Metric Volume Units	207	(1)
Metric Volume Practical Applications	207	(1)
Customary and Metric Units of Capacity	208	(1)
Customary and Metric Capacity Practical Applications	209	(1)
Customary and Metric Units of Weight (Mass)	210	(2)
Customary and Metric Weight Practical Applications	212	(1)
Compound Units	212	(2)
Compound Units Practical Applications	214	(8)
Unit Exercise and Problem Review	216	(6)
Steel Rules and Vernier Calipers	222	(13)
Types of Steel Rules	222	(1)
Reading Fractional Measurements	222	(2)
Measurements that do not Fall on Rule Graduations	224	(1)
Reading Decimal-Inch Measurements	225	(1)
Reading Metric Measurements	226	(1)
Vernier Calipers: Types and Description	227	(2)
Reading Measurements on a Customary Vernier Caliper	229	(2)
Reading Measurements on a Metric Vernier Caliper	231	(4)
Unit Exercise and Problem Review	233	(2)
Micrometers	235	(12)
Description of a Customary Outside Micrometer	235	(1)
Reading a Customary Micrometer	236	(1)
The Customary Vernier Micrometer	237	(1)
Reading a Customary Vernier Micrometer	238	(2)
Description of a Metric Micrometer	240	(1)
Reading a Metric Micrometer	240	(1)
The Metric Vernier Micrometer	241	(1)
Reading a Metric Vernier Micrometer	242	(5)
Unit Exercise and Problem Review	244	(3)
SECTION III Fundamentals of Algebra	247	(168)
Introduction to Algebra	248	(11)
Symbolism	248	(1)
Algebraic Expressions	248	(3)
Evaluation of Algebraic Expressions	251	(8)
Unit Exercise and Problem Review	256	(3)
Signed Numbers	259	(21)
Meaning of Signed Numbers	259	(1)
The Number Scale	260	(2)
Operations Using Signed Numbers	262	(1)
Absolute Value	262	(1)
Addition of Signed Numbers	263	(3)
Subtraction of Signed Numbers	266	(1)
Multiplication of Signed Numbers	267	(1)
Division of Signed Numbers	268	(1)
Powers of Signed Numbers	269	(3)
Roots of Signed Numbers	272	(2)
Combined Operations of Signed Numbers	274	(6)
Unit Exercise and Problem Review	276	(4)
Basic Algebraic Operations	280	(39)
Definitions	280	(1)
Addition	281	(2)
Subtraction	283	(3)
Multiplication	286	(3)
Division	289	(4)
Powers	293	(2)
Roots	295	(3)
Removal of Parentheses	298	(1)
Combined Operations	298	(2)
Scientific Notation	300	(5)
Metric Prefixes Applied to Very Large and Very Small Numbers	305	(3)
Basic Structure of the Binary Numeration System	308	(11)
Unit Exercise and Problem Review	312	(7)
Simple Equations	319	(23)
Expression of Equality	319	(1)
Writing Equations from Word Statements	320	(2)
Checking the Equation	322	(2)
Principles of Equality	324	(1)
Solution of Equations by the Subtraction Principle of Equality	324	(3)
Solution of Equations by the Addition Principle of Equality	327	(3)
Solution of Equations by the Division Principle of Equality	330	(2)
Solution of Equations by the Multiplication Principle of Equality	332	(3)
Solution of Equations by the Root Principle of Equality	335	(2)
Solution of Equations by the Power Principle of Equality	337	(5)
Unit Exercise and Problem Review	339	(3)
Complex Equations	342	(14)
Equations Consisting of Combined Operations	342	(4)
Solving for the Unknown in Formulas	346	(1)
Substituting Values Directly in Given Formulas	346	(3)
Rearranging Formulas	349	(7)
Unit Exercise and Problem Review	353	(3)
Ratio and Proportion	356	(16)
Description of Ratios	356	(1)
Order of Terms of Ratios	357	(2)
Description of Proportions	359	(4)
Direct Proportions	363	(2)
Inverse Proportions	365	(7)
Unit Exercise and Problem Review	368	(4)
The Cartesian Coordinate System and Graphs of Linear Equations	372	(9)
Description of the Cartesian (Rectangular) Coordinate System	372	(1)
Graphing a Linear Equation	373	(2)
Slope of a Linear Equation	375	(1)
Slope Intercept Equation of a Straight Line	376	(1)
Determining an Equation, Given Two Points	377	(1)
Describing a Straight Line	378	(3)
Unit Exercise and Problem Review	379	(2)
Systems of Equations	381	(16)
Graphical Method of Solving Systems of Equations	381	(2)
Substitution Method of Solving Systems of Equations	383	(1)
Addition or Subtraction Method of Solving Systems of Equations	384	(4)
Types of Systems of Equations	388	(1)
Writing and Solving Systems of Equations From Word Statements, Number Problems, and Practical Applications	389	(8)
Unit Exercise and Problem Review	395	(2)
Quadratic Equations	397	(18)
General or Standard Form of Quadratic Equations	397	(1)
Incomplete Quadratic Equations	398	(4)
Complete Quadratic Equations	402	(2)
Practical Applications of Complete Quadratic Equations	404	(5)
Word Problems Involving Complete Quadratic Equations. Equations Not Given	409	(6)
Unit Exercise and Problem Review	413	(2)
SECTION IV Fundamentals of Plane Geometry	415	(120)
Introduction to Plane Geometry	416	(6)
Plane Geometry	416	(1)
Axioms and Postulates	417	(3)
Points and Lines	420	(2)
Unit Exercise	421	(1)
Angular Measure	422	(20)
Units of Angular Measure	422	(1)
Units of Angular Measure in Degrees, Minutes, and Seconds	423	(1)
Expressing Degrees, Minutes, and Seconds as Decimal Degrees	424	(1)
Expressing Decimal Degrees as Degrees, Minutes, and Seconds	424	(2)
Arithmetic Operations on Angular Measure in Degrees, Minutes, and Seconds	426	(8)
Simple Semicircular Protractor	434	(1)
Circle Graphs	435	(3)
Complements and Supplements of Scale Readings	438	(4)
Unit Exercise and Problem Review	439	(3)
Angular Geometric Principles	442	(13)
Naming Angles	442	(1)
Types of Angles	442	(1)
Angles Formed by a Transversal	443	(2)
Theorems and Corollaries	445	(10)
Unit Exercise and Problem Review	452	(3)
Triangles	455	(16)
Types of Triangles	456	(2)
Angles of a Triangle	458	(4)
Isosceles and Equilateral Triangles	462	(1)
Isosceles Triangle Practical Application	462	(1)
Equilateral Triangle Practical Application	463	(1)
The Pythagorean Theorem	464	(1)
Pythagorean Theorem Practical Applications	464	(7)
Unit Exercise and Problem Review	467	(4)
Congruent and Similar Figures	471	(14)
Congruent Figures	471	(2)
Similar Figures	473	(3)
Similar Triangles Practical Applications	476	(9)
Unit Exercise and Problem Review	481	(4)
Polygons	485	(14)
Types of Polygons	485	(2)
Types of Quadrilaterals	487	(2)
Polygon Interior and Exterior Angles	489	(1)
Polygon Interior and Exterior Angles Practical Applications	489	(5)
Trapezoid Median Practical Applications	494	(5)
Unit Exercise and Problem Review	496	(3)
Circles	499	(36)
Definitions	499	(2)
Circumference Formula	501	(1)
Arc Length Formula	502	(2)
Radian Measure	504	(2)
Circle Postulates	506	(1)
Chords, Arcs, and Central Angles	507	(1)
Circle Chord Bisector Practical Application	508	(3)
Circle Tangents and Chord Segments	511	(1)
Circle Tangent Practical Application	512	(1)
Tangents From a Common Point Practical Application	513	(3)
Angles Formed Inside and on a Circle	516	(1)
Inscribed Angles Practical Application	516	(1)
Tangent and Chord Practical Application	517	(3)
Angles Outside a Circle	520	(1)
Internally and Externally Tangent Circles	521	(1)
Internally Tangent Circles Practical Application	522	(2)
Externally Tangent Circles Practical Application	524	(11)
Unit Exercise and Problem Review	528	(7)
SECTION V Geometric Figures: Areas and Volumes	535	(76)
Areas of Common Polygons	536	(22)
Areas of Rectangles	536	(3)
Areas of Parallelograms	539	(4)
Areas of Trapezoids	543	(4)
Areas of Triangles Given the Base and Height	547	(2)
Areas of Triangles Given Three Sides	549	(9)
Unit Exercise and Problem Review	553	(5)
Areas of Circles, Sectors, Segments, and Ellipses	558	(14)
Areas of Circles	558	(1)
Ratio of Two Circles	559	(3)
Areas of Sectors	562	(2)
Areas of Segments	564	(2)
Areas of Ellipses	566	(6)
Unit Exercise and Problem Review	568	(4)
Prisms and Cylinders: Volumes, Surface Areas, and Weights	572	(13)
Prisms	572	(1)
Volumes of Prisms	572	(3)
Cylinders	575	(1)
Volumes of Cylinders	576	(2)
Computing Heights and Bases of Prisms and Cylinders	578	(2)
Lateral Areas and Surface Areas of Right Prisms and Cylinders	580	(5)
Unit Exercise and Problem Review	583	(2)
Pyramids and Cones: Volumes, Surface Areas, and Weights	585	(16)
Pyramids	585	(1)
Cones	586	(1)
Volumes of Regular Pyramids and Right Circular Cones	586	(2)
Computing Heights and Bases of Regular Pyramids and Right Circular Cones	588	(1)
Lateral Areas and Surface Areas of Regular Pyramids and Right Circular Cones	589	(3)
Frustums of Pyramids and Cones	592	(1)
Volumes of Frustums of Regular Pyramids and Right Circular Cones	593	(2)
Lateral Areas and Surface Areas of Frustums of Regular Pyramids and Right Circular Cones	595	(6)
Unit Exercise and Problem Review	599	(2)
Spheres and Composite Figures: Volumes, Surface Areas, and Weights	601	(10)
Spheres	601	(1)
Surface Area of a Sphere	602	(1)
Volume of a Sphere	602	(2)
Volumes and Surface Areas of Composite Solid Figures	604	(7)
Unit Exercise and Problem Review	609	(2)
SECTION VI Fundamentals of Trigonometry	611	(108)
Introduction to Trigonometric Functions	612	(10)
Ratio of Right Triangle Sides	612	(1)
Identifying Right Triangle Sides by Name	613	(1)
Trigonometric Functions: Ratio Method	614	(2)
Customary and Metric Units of Angular Measure	616	(1)
Determining Functions of Given Angles and Determining Angles of Given Functions	616	(6)
Unit Exercise and Problem Review	620	(2)
Trigonometric Functions with Right Triangles	622	(12)
Variation of Functions	622	(2)
Functions of Complementary Angles	624	(2)
Determining an Unknown Angle When Two Sides of a Right Triangle Are Known	626	(2)
Determining an Unknown Side When an Acute Angle and One Side of a Right Triangle are Known	628	(6)
Unit Exercise and Problem Review	632	(2)
Practical Applications with Right Triangles	634	(28)
Solving Problems Stated in Word Form	634	(5)
Solving Problems Given in Picture Form that Require Auxiliary Lines	639	(9)
Solving Complex Problems that Require Auxiliary Lines	648	(14)
Unit Exercise and Problem Review	657	(5)
Functions of Any Angle, Oblique Triangles	662	(35)
Cartesian (Rectangular) Coordinate System	662	(1)
Determining Functions of Angles in Any Quadrant	663	(3)
Alternating Current Applications	666	(3)
Determining Functions of Angles Greater Than 360°	669	(1)
Instantaneous Voltage Related to Time Application	670	(1)
Solving Oblique Triangles	671	(1)
Law of Sines	671	(1)
Solving Problems Given Two Angles and a Side, Using the Law of Sines	672	(2)
Solving Problems Given Two Sides and an Angle Opposite One of the Given Sides, Using the Law of Sines	674	(4)
Law of Cosines (Given Two Sides and the Included Angle)	678	(1)
Solving Problems Given Two Sides and the Included Angle, Using the Law of Cosines	678	(3)
Law of Cosines (Given Three Sides)	681	(1)
Solving Problems Given Three Sides, Using the Law of Cosines	682	(3)
Practical Applications of Oblique Trigonometry	685	(12)
Unit Exercise and Problem Review	692	(5)
Vectors	697	(22)
Scalar and Vector Quantities	697	(1)
Description and Naming Vectors	697	(1)
Vector Ordered Pair Notation	698	(1)
Vector Length and Angle Notation	699	(1)
Adding Vectors	699	(2)
Graphic Addition of Vectors	701	(4)
Addition of Vectors Using Trigonometry	705	(6)
General (Component Vector) Procedure for Vectors Using Trigonometry	711	(8)
Unit Exercise and Problem Review	716	(3)
Appendix A United States Customary and Metric Units of Measure	719	(2)
Appendix B Formulas for Areas (A) of Plane Figures	721	(1)
Appendix C Formulas for Volumes and Areas of Solid Figures	722	(1)
Appendix D Answers to Odd-Numbered Exercises	723	(32)
Index	755