Instructor's Solutions Manual for
Basic Technical Mathematics and
Basic Technical Mathematics with Calculus, 12th Edition
Chapter 1 Basic Algebraic Operations .....................................................................................1
Chapter 2 Geometry..............................................................................................................104
Chapter 3 Functions and Graphs ..........................................................................................171
Chapter 4 The Trigonometric Functions ..............................................................................259
Chapter 5 Systems of Linear Equations; Determinants ........................................................346
Chapter 6 Factoring and Fractions........................................................................................490
Chapter 7 Quadratic Equations .............................................................................................581
Chapter 8 Trigonometric Functions of Any Angle ...............................................................666
Chapter 9 Vectors and Oblique Triangles ............................................................................723
Chapter 10 Graphs of the Trigonometric Functions ...............................................................828
Chapter 11 Exponents and Radicals .......................................................................................919
Chapter 12 Complex Numbers .............................................................................................1001
Chapter 13 Exponential and Logarithmic Functions ............................................................1090
Chapter 14 Additional Types of Equations and Systems of Equations ................................1183
Chapter 15 Equations of Higher Degree...............................................................................1290
Chapter 16 Matrices; Systems of Linear Equations .............................................................1356
Chapter 17 Inequalities .........................................................................................................1477
Chapter 18 Variation ............................................................................................................1598
Chapter 19 Sequences and the Binomial Theorem ...............................................................1634
Chapter 20 Additional Topics in Trigonometry ...................................................................1696
,Chapter 21 Plane Analytic Geometry ...................................................................................1812
Chapter 22 Introduction to Statistics ....................................................................................2052
Chapter 23 The Derivative ...................................................................................................2126
Chapter 24 Applications of the Derivative ...........................................................................2310
Chapter 25 Integration ..........................................................................................................2487
Chapter 26 Applications of Integration ................................................................................2572
Chapter 27 Differentiation of Transcendental Functions .....................................................2701
Chapter 28 Methods of Integration .......................................................................................2839
Chapter 29 Partial Derivatives and Double Integrals ...........................................................2991
Chapter 30 Expansion of Functions in Series .......................................................................3058
Chapter 31 Differential Equations ........................................................................................3181
, Chapter 1
Basic Algebraic Operations
1.1 Numbers
7 12
1. The numbers –7 and 12 are integers. They are also rational numbers since they can be written as and .
1 1
2. The absolute value of –6 is 6, and the absolute value of –7 is 7. We write these as 6 6 and 7 7 .
3. 6 4 ; –6 is to the left of –4.
–7 –6 –5 –4 –3 –2 –1 0 1
3 1 2 2
4. The reciprocal of is 1 .
2 3/ 2 3 3
3
5. 3 is an integer, rational , and real.
1
4 is imaginary.
7
6. is irrational (because 7 is an irrational number) and real.
3
6
6 is an integer, rational , and real.
1
7. is irrational (because is an irrational number) and real.
6
1
is rational and real.
8
8. 6 is imaginary.
233
2.33 is rational and real.
100
9. 3 3
3 3
2 2
10. 0.857 0.857
2 2
19 19
4 4
1
, 2 Chapter 1 Basic Algebraic Operations
11. 6 8 ; 6 is to the left of 8.
3 4 5 6 7 8 9 10 11
12. 7 5 ; 7 is to the right of 5.
3 4 5 6 7 8 9 10 11
13. 3.1416; (3.1415926) is to the left of 3.1416.
( ) (3.1416)
3.141592 3.1416
14. 4 0 ; –4 is to the left of 0.
–6 –5 –4 –3 –2 –1 0 1 2
15. 4 3 ; –4 is to the left of 3 , 3 3 3 .
–6 –5 –4 –3 –2 –1 0 1 2
16. 2 1.42; ( 2 1.414. 1.414), 2 is to the right of –1.42.
–1.44 –1.43 –1.42 –1.41 –1.40
2 3 2 3
17. ; 0.666 is to the right of 0.75 .
3 4 3 4
–0.8 –0.7 –0.6 –0.5 –0.4
18. 0.6 0.2 ; –0.6 is to the left of 0.2.
–0.6 –0.5 –0.4 –0.3 –0.2 –0.1 0 0.1 0.2
Basic Technical Mathematics and
Basic Technical Mathematics with Calculus, 12th Edition
Chapter 1 Basic Algebraic Operations .....................................................................................1
Chapter 2 Geometry..............................................................................................................104
Chapter 3 Functions and Graphs ..........................................................................................171
Chapter 4 The Trigonometric Functions ..............................................................................259
Chapter 5 Systems of Linear Equations; Determinants ........................................................346
Chapter 6 Factoring and Fractions........................................................................................490
Chapter 7 Quadratic Equations .............................................................................................581
Chapter 8 Trigonometric Functions of Any Angle ...............................................................666
Chapter 9 Vectors and Oblique Triangles ............................................................................723
Chapter 10 Graphs of the Trigonometric Functions ...............................................................828
Chapter 11 Exponents and Radicals .......................................................................................919
Chapter 12 Complex Numbers .............................................................................................1001
Chapter 13 Exponential and Logarithmic Functions ............................................................1090
Chapter 14 Additional Types of Equations and Systems of Equations ................................1183
Chapter 15 Equations of Higher Degree...............................................................................1290
Chapter 16 Matrices; Systems of Linear Equations .............................................................1356
Chapter 17 Inequalities .........................................................................................................1477
Chapter 18 Variation ............................................................................................................1598
Chapter 19 Sequences and the Binomial Theorem ...............................................................1634
Chapter 20 Additional Topics in Trigonometry ...................................................................1696
,Chapter 21 Plane Analytic Geometry ...................................................................................1812
Chapter 22 Introduction to Statistics ....................................................................................2052
Chapter 23 The Derivative ...................................................................................................2126
Chapter 24 Applications of the Derivative ...........................................................................2310
Chapter 25 Integration ..........................................................................................................2487
Chapter 26 Applications of Integration ................................................................................2572
Chapter 27 Differentiation of Transcendental Functions .....................................................2701
Chapter 28 Methods of Integration .......................................................................................2839
Chapter 29 Partial Derivatives and Double Integrals ...........................................................2991
Chapter 30 Expansion of Functions in Series .......................................................................3058
Chapter 31 Differential Equations ........................................................................................3181
, Chapter 1
Basic Algebraic Operations
1.1 Numbers
7 12
1. The numbers –7 and 12 are integers. They are also rational numbers since they can be written as and .
1 1
2. The absolute value of –6 is 6, and the absolute value of –7 is 7. We write these as 6 6 and 7 7 .
3. 6 4 ; –6 is to the left of –4.
–7 –6 –5 –4 –3 –2 –1 0 1
3 1 2 2
4. The reciprocal of is 1 .
2 3/ 2 3 3
3
5. 3 is an integer, rational , and real.
1
4 is imaginary.
7
6. is irrational (because 7 is an irrational number) and real.
3
6
6 is an integer, rational , and real.
1
7. is irrational (because is an irrational number) and real.
6
1
is rational and real.
8
8. 6 is imaginary.
233
2.33 is rational and real.
100
9. 3 3
3 3
2 2
10. 0.857 0.857
2 2
19 19
4 4
1
, 2 Chapter 1 Basic Algebraic Operations
11. 6 8 ; 6 is to the left of 8.
3 4 5 6 7 8 9 10 11
12. 7 5 ; 7 is to the right of 5.
3 4 5 6 7 8 9 10 11
13. 3.1416; (3.1415926) is to the left of 3.1416.
( ) (3.1416)
3.141592 3.1416
14. 4 0 ; –4 is to the left of 0.
–6 –5 –4 –3 –2 –1 0 1 2
15. 4 3 ; –4 is to the left of 3 , 3 3 3 .
–6 –5 –4 –3 –2 –1 0 1 2
16. 2 1.42; ( 2 1.414. 1.414), 2 is to the right of –1.42.
–1.44 –1.43 –1.42 –1.41 –1.40
2 3 2 3
17. ; 0.666 is to the right of 0.75 .
3 4 3 4
–0.8 –0.7 –0.6 –0.5 –0.4
18. 0.6 0.2 ; –0.6 is to the left of 0.2.
–0.6 –0.5 –0.4 –0.3 –0.2 –0.1 0 0.1 0.2
