INSTRUCTOR’S SOLUTIONS
MANUAL
ST
TIM BRITT
Jackson State Community College
U
VI
ALGEBRA AND
A
TRIGONOMETRY
_A
E LEVENTH E DITION
PP
Michael Sullivan
RO
Chicago State University
VE
D
?
, Table of Contents
Chapter R Review
ST
R.1 Real Numbers ........................................................................................................................... 1
R.2 Algebra Essentials .................................................................................................................... 5
R.3 Geometry Essentials ............................................................................................................... 11
R.4 Polynomials ............................................................................................................................ 16
R.5 Factoring Polynomials ............................................................................................................ 23
R.6 Synthetic Division .................................................................................................................. 28
U
R.7 Rational Expressions .............................................................................................................. 30
R.8 nth Roots; Rational Exponents ............................................................................................... 40
VI
Chapter 1 Equations and Inequalities
1.1 Linear Equations ..................................................................................................................... 50
1.2 Quadratic Equations ................................................................................................................ 68
1.3 Complex Numbers; Quadratic Equations in the Complex Number System............................ 87
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations ............................... 93
A
1.5 Solving Inequalities ............................................................................................................... 116
1.6 Equations and Inequalities Involving Absolute Value .......................................................... 127
1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ...... 137
_A
Chapter Review ............................................................................................................................ 145
Chapter Test ................................................................................................................................. 154
Chapter Projects ........................................................................................................................... 156
Chapter 2 Graphs
PP
2.1 The Distance and Midpoint Formulas ................................................................................... 157
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ............................................. 170
2.3 Lines ...................................................................................................................................... 184
2.4 Circles ................................................................................................................................... 202
2.5 Variation................................................................................................................................ 216
RO
Chapter Review ............................................................................................................................ 222
Chapter Test ................................................................................................................................. 228
Cumulative Review ...................................................................................................................... 230
Chapter Project ............................................................................................................................. 232
Chapter 3 Functions and Their Graphs
VE
3.1 Functions ............................................................................................................................... 233
3.2 The Graph of a Function ....................................................................................................... 251
3.3 Properties of Functions.......................................................................................................... 260
3.4 Library of Functions; Piecewise-defined Functions .............................................................. 277
3.5 Graphing Techniques: Transformations ................................................................................ 289
3.6 Mathematical Models: Building Functions ........................................................................... 307
Chapter Review ............................................................................................................................ 315
D
Chapter Test ................................................................................................................................. 322
Cumulative Review ...................................................................................................................... 325
Chapter Projects ........................................................................................................................... 329
?
, Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models ............................................................... 331
4.2 Building Linear Functions from Data ................................................................................... 342
4.3 Quadratic Functions and Their Properties ............................................................................. 348
ST
4.4 Build Quadratic Models from Verbal Descriptions and from Data ...................................... 371
4.5 Inequalities Involving Quadratic Functions .......................................................................... 379
Chapter Review ............................................................................................................................ 399
Chapter Test ................................................................................................................................. 407
Cumulative Review ...................................................................................................................... 409
U
Chapter Projects ........................................................................................................................... 412
Chapter 5 Polynomial and Rational Functions
VI
5.1 Polynomial Functions............................................................................................................ 415
5.2 Graphing Polynomial Functions; Models............................................................................... 425
5.3 Properties of Rational Functions ........................................................................................... 441
5.4 The Graph of a Rational Function ......................................................................................... 451
5.5 Polynomial and Rational Inequalities.................................................................................... 507
A
5.6 The Real Zeros of a Polynomial Function............................................................................. 528
5.7 Complex Zeros; Fundamental Theorem of Algebra .............................................................. 559
Chapter Review ............................................................................................................................ 568
_A
Chapter Test ................................................................................................................................. 583
Cumulative Review ...................................................................................................................... 587
Chapter Projects ........................................................................................................................... 592
Chapter 6 Exponential and Logarithmic Functions
PP
6.1 Composite Functions ............................................................................................................. 594
6.2 One-to-One Functions; Inverse Functions ............................................................................ 612
6.3 Exponential Functions ........................................................................................................... 634
6.4 Logarithmic Functions .......................................................................................................... 655
6.5 Properties of Logarithms ....................................................................................................... 677
6.6 Logarithmic and Exponential Equations ............................................................................... 686
RO
6.7 Financial Models ................................................................................................................... 706
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models .............................................................................................................. 714
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................... 723
Chapter Review ............................................................................................................................ 729
Chapter Test ................................................................................................................................. 741
Cumulative Review ...................................................................................................................... 745
VE
Chapter Projects ........................................................................................................................... 748
D
?
, Chapter 7 Trigonometric Functions
7.1 Angles, Arc Length, and Circular Motion ............................................................................. 751
7.2 Right Triangle Trigonometry ................................................................................................ 760
7.3 Computing the Values of Trigonometric Functions of Acute Angles ................................... 776
7.4 Trigonometric Functions of Any Angle ................................................................................ 789
ST
7.5 Unit Circle Approach: Properties of the Trigonometric Functions ....................................... 805
7.6 Graphs of the Sine and Cosine Functions ............................................................................. 814
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions .................................... 836
7.8 Phase Shift; Sinusoidal Curve Fitting ................................................................................... 846
Chapter Review ............................................................................................................................ 857
Chapter Test ................................................................................................................................. 866
U
Cumulative Review ...................................................................................................................... 870
Chapter Projects ........................................................................................................................... 874
VI
Chapter 8 Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions ................................................................ 877
8.2 The Inverse Trigonometric Functions (Continued) ............................................................... 890
8.3 Trigonometric Equations ....................................................................................................... 902
A
8.4 Trigonometric Identities ........................................................................................................ 923
8.5 Sum and Difference Formulas............................................................................................... 936
8.6 Double-angle and Half-angle Formulas ................................................................................ 961
8.7 Product-to-Sum and Sum-to-Product Formulas .................................................................... 987
_A
Chapter Review .......................................................................................................................... 1000
Chapter Test ............................................................................................................................... 1015
Cumulative Review .................................................................................................................... 1020
Chapter Projects ......................................................................................................................... 1026
PP
Chapter 9 Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles .............................................................................. 1030
9.2 The Law of Sines ................................................................................................................ 1038
9.3 The Law of Cosines ............................................................................................................ 1053
9.4 Area of a Triangle ............................................................................................................... 1065
RO
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves ........................................ 1075
Chapter Review .......................................................................................................................... 1085
Chapter Test ............................................................................................................................... 1091
Cumulative Review .................................................................................................................... 1094
Chapter Projects ......................................................................................................................... 1100
Chapter 10 Polar Coordinates; Vectors
VE
10.1 Polar Coordinates .............................................................................................................. 1104
10.2 Polar Equations and Graphs .............................................................................................. 1113
10.3 The Complex Plane; De Moivre’s Theorem ..................................................................... 1143
10.4 Vectors .............................................................................................................................. 1156
10.5 The Dot Product ................................................................................................................ 1169
D
Chapter Review .......................................................................................................................... 1175
Chapter Test ............................................................................................................................... 1183
Cumulative Review .................................................................................................................... 1186
Chapter Projects ......................................................................................................................... 1189
?
MANUAL
ST
TIM BRITT
Jackson State Community College
U
VI
ALGEBRA AND
A
TRIGONOMETRY
_A
E LEVENTH E DITION
PP
Michael Sullivan
RO
Chicago State University
VE
D
?
, Table of Contents
Chapter R Review
ST
R.1 Real Numbers ........................................................................................................................... 1
R.2 Algebra Essentials .................................................................................................................... 5
R.3 Geometry Essentials ............................................................................................................... 11
R.4 Polynomials ............................................................................................................................ 16
R.5 Factoring Polynomials ............................................................................................................ 23
R.6 Synthetic Division .................................................................................................................. 28
U
R.7 Rational Expressions .............................................................................................................. 30
R.8 nth Roots; Rational Exponents ............................................................................................... 40
VI
Chapter 1 Equations and Inequalities
1.1 Linear Equations ..................................................................................................................... 50
1.2 Quadratic Equations ................................................................................................................ 68
1.3 Complex Numbers; Quadratic Equations in the Complex Number System............................ 87
1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations ............................... 93
A
1.5 Solving Inequalities ............................................................................................................... 116
1.6 Equations and Inequalities Involving Absolute Value .......................................................... 127
1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ...... 137
_A
Chapter Review ............................................................................................................................ 145
Chapter Test ................................................................................................................................. 154
Chapter Projects ........................................................................................................................... 156
Chapter 2 Graphs
PP
2.1 The Distance and Midpoint Formulas ................................................................................... 157
2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ............................................. 170
2.3 Lines ...................................................................................................................................... 184
2.4 Circles ................................................................................................................................... 202
2.5 Variation................................................................................................................................ 216
RO
Chapter Review ............................................................................................................................ 222
Chapter Test ................................................................................................................................. 228
Cumulative Review ...................................................................................................................... 230
Chapter Project ............................................................................................................................. 232
Chapter 3 Functions and Their Graphs
VE
3.1 Functions ............................................................................................................................... 233
3.2 The Graph of a Function ....................................................................................................... 251
3.3 Properties of Functions.......................................................................................................... 260
3.4 Library of Functions; Piecewise-defined Functions .............................................................. 277
3.5 Graphing Techniques: Transformations ................................................................................ 289
3.6 Mathematical Models: Building Functions ........................................................................... 307
Chapter Review ............................................................................................................................ 315
D
Chapter Test ................................................................................................................................. 322
Cumulative Review ...................................................................................................................... 325
Chapter Projects ........................................................................................................................... 329
?
, Chapter 4 Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models ............................................................... 331
4.2 Building Linear Functions from Data ................................................................................... 342
4.3 Quadratic Functions and Their Properties ............................................................................. 348
ST
4.4 Build Quadratic Models from Verbal Descriptions and from Data ...................................... 371
4.5 Inequalities Involving Quadratic Functions .......................................................................... 379
Chapter Review ............................................................................................................................ 399
Chapter Test ................................................................................................................................. 407
Cumulative Review ...................................................................................................................... 409
U
Chapter Projects ........................................................................................................................... 412
Chapter 5 Polynomial and Rational Functions
VI
5.1 Polynomial Functions............................................................................................................ 415
5.2 Graphing Polynomial Functions; Models............................................................................... 425
5.3 Properties of Rational Functions ........................................................................................... 441
5.4 The Graph of a Rational Function ......................................................................................... 451
5.5 Polynomial and Rational Inequalities.................................................................................... 507
A
5.6 The Real Zeros of a Polynomial Function............................................................................. 528
5.7 Complex Zeros; Fundamental Theorem of Algebra .............................................................. 559
Chapter Review ............................................................................................................................ 568
_A
Chapter Test ................................................................................................................................. 583
Cumulative Review ...................................................................................................................... 587
Chapter Projects ........................................................................................................................... 592
Chapter 6 Exponential and Logarithmic Functions
PP
6.1 Composite Functions ............................................................................................................. 594
6.2 One-to-One Functions; Inverse Functions ............................................................................ 612
6.3 Exponential Functions ........................................................................................................... 634
6.4 Logarithmic Functions .......................................................................................................... 655
6.5 Properties of Logarithms ....................................................................................................... 677
6.6 Logarithmic and Exponential Equations ............................................................................... 686
RO
6.7 Financial Models ................................................................................................................... 706
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
and Decay Models .............................................................................................................. 714
6.9 Building Exponential, Logarithmic, and Logistic Models from Data ................................... 723
Chapter Review ............................................................................................................................ 729
Chapter Test ................................................................................................................................. 741
Cumulative Review ...................................................................................................................... 745
VE
Chapter Projects ........................................................................................................................... 748
D
?
, Chapter 7 Trigonometric Functions
7.1 Angles, Arc Length, and Circular Motion ............................................................................. 751
7.2 Right Triangle Trigonometry ................................................................................................ 760
7.3 Computing the Values of Trigonometric Functions of Acute Angles ................................... 776
7.4 Trigonometric Functions of Any Angle ................................................................................ 789
ST
7.5 Unit Circle Approach: Properties of the Trigonometric Functions ....................................... 805
7.6 Graphs of the Sine and Cosine Functions ............................................................................. 814
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions .................................... 836
7.8 Phase Shift; Sinusoidal Curve Fitting ................................................................................... 846
Chapter Review ............................................................................................................................ 857
Chapter Test ................................................................................................................................. 866
U
Cumulative Review ...................................................................................................................... 870
Chapter Projects ........................................................................................................................... 874
VI
Chapter 8 Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions ................................................................ 877
8.2 The Inverse Trigonometric Functions (Continued) ............................................................... 890
8.3 Trigonometric Equations ....................................................................................................... 902
A
8.4 Trigonometric Identities ........................................................................................................ 923
8.5 Sum and Difference Formulas............................................................................................... 936
8.6 Double-angle and Half-angle Formulas ................................................................................ 961
8.7 Product-to-Sum and Sum-to-Product Formulas .................................................................... 987
_A
Chapter Review .......................................................................................................................... 1000
Chapter Test ............................................................................................................................... 1015
Cumulative Review .................................................................................................................... 1020
Chapter Projects ......................................................................................................................... 1026
PP
Chapter 9 Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles .............................................................................. 1030
9.2 The Law of Sines ................................................................................................................ 1038
9.3 The Law of Cosines ............................................................................................................ 1053
9.4 Area of a Triangle ............................................................................................................... 1065
RO
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves ........................................ 1075
Chapter Review .......................................................................................................................... 1085
Chapter Test ............................................................................................................................... 1091
Cumulative Review .................................................................................................................... 1094
Chapter Projects ......................................................................................................................... 1100
Chapter 10 Polar Coordinates; Vectors
VE
10.1 Polar Coordinates .............................................................................................................. 1104
10.2 Polar Equations and Graphs .............................................................................................. 1113
10.3 The Complex Plane; De Moivre’s Theorem ..................................................................... 1143
10.4 Vectors .............................................................................................................................. 1156
10.5 The Dot Product ................................................................................................................ 1169
D
Chapter Review .......................................................................................................................... 1175
Chapter Test ............................................................................................................................... 1183
Cumulative Review .................................................................................................................... 1186
Chapter Projects ......................................................................................................................... 1189
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