3/1/2026, 1:11:30 PM Solutions for Basic Technical Solutions
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
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
3/1/2026, 1:06:21 PM Solutions for Basic Technical Solutions
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
,3/1/2026, 1:11:30 PM Solutions for Basic Technical Solutions
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
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
3/1/2026, 1:06:21 PM Solutions for Basic Technical Solutions
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
,3/1/2026, 1:11:30 PM Solutions for Basic Technical Solutions
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
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
3/1/2026, 1:06:21 PM Solutions for Basic Technical Solutions
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
, 3/1/2026, 1:11:30 PM Solutions for Basic Technical Solutions
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
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
3/1/2026, 1:06:21 PM Solutions for Basic Technical Solutions
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
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
3/1/2026, 1:06:21 PM Solutions for Basic Technical Solutions
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
,3/1/2026, 1:11:30 PM Solutions for Basic Technical Solutions
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
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
3/1/2026, 1:06:21 PM Solutions for Basic Technical Solutions
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
,3/1/2026, 1:11:30 PM Solutions for Basic Technical Solutions
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
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
3/1/2026, 1:06:21 PM Solutions for Basic Technical Solutions
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
, 3/1/2026, 1:11:30 PM Solutions for Basic Technical Solutions
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
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
3/1/2026, 1:06:21 PM Solutions for Basic Technical Solutions
Mathematics
for Basic
with Calculus,
Technical12th
Mathematics
Edition bywith
Allyn
Calculus,
J. Washington.pdf
12th Edition by Allyn J. Washington.pdf
