, SOLUTIONS
MANUAL
BEVERLY FUSFIELD
PRECALCULUS
A U NIT C IRCLE A PPROACH
FOURTH EDITION
J. S. Ratti
Marcus McWaters
Leslaw A. Skrzypek
with
Jessica Bernards
Wendy Fresh
, CONTENTS
Chapter 1 Graphs and Functions
1.1 The Coordinate Plane ................................................................................... 1
1.2 Graphs of Equations ................................................................................... 11
1.3 Lines ........................................................................................................... 24
1.4 Functions .................................................................................................... 39
1.5 Properties of Functions............................................................................... 49
1.6 A Library of Functions ............................................................................... 59
1.7 Transformations of Functions .................................................................... 71
1.8 Combining Functions; Composite Functions ............................................. 88
1.9 Inverse Functions ..................................................................................... 109
Chapter 1 Key Ideas at a Glance ........................................................................... 125
Chapter 1 Review Exercises .................................................................................. 127
Chapter 1 Practice Test A ...................................................................................... 138
Chapter 1 Practice Test B ...................................................................................... 140
Chapter 2 Polynomial and Rational Functions
2.1 Quadratic Functions ................................................................................. 141
2.2 Polynomial Functions ............................................................................... 163
2.3 Dividing Polynomials and the Rational Zeros Test .................................. 180
2.4 Rational Functions.................................................................................... 203
2.5 Polynomial and Rational Inequalities....................................................... 230
2.6 Zeros of a Polynomial Function ............................................................... 260
2.7 Variation ................................................................................................... 273
Chapter 2 Key Ideas at a Glance ........................................................................... 278
Chapter 2 Review Exercises .................................................................................. 281
Chapter 2 Practice Test A ...................................................................................... 298
Chapter 2 Practice Test B ...................................................................................... 299
Cumulative Review Exercises (Chapters 1−2) ...................................................... 301
Chapter 3 Exponential and Logarithmic Functions
3.1 Exponential Functions .............................................................................. 305
3.2 Logarithmic Functions ............................................................................. 318
3.3 Rules of Logarithms ................................................................................. 332
3.4 Exponential and Logarithmic Equations and Inequalities ........................ 344
3.5 Logarithmic Scales; Modeling ................................................................. 359
Chapter 3 Key Ideas at a Glance ........................................................................... 370
Chapter 3 Review Exercises .................................................................................. 370
Chapter 3 Practice Test A ...................................................................................... 379
Chapter 3 Practice Test B ...................................................................................... 380
Cumulative Review Exercises (Chapters 1−3) ...................................................... 381
Chapter 4 Trigonometric Functions
4.1 Angles and Their Measure ....................................................................... 385
4.2 The Unit Circle; Trigonometric Functions of Real Numbers ................... 392
4.3 Trigonometric Functions of Angles ......................................................... 406
4.4 Graphs of the Sine and Cosine Functions................................................. 418
4.5 Graphs of the Other Trigonometric Functions ......................................... 437
4.6 Inverse Trigonometric Functions ............................................................. 452
Chapter 4 Key Ideas at a Glance ........................................................................... 461
Chapter 4 Review Exercises .................................................................................. 463
Copyright © 2023 Pearson Education Inc.
, Chapter 4 Practice Test A ...................................................................................... 467
Chapter 4 Practice Test B ...................................................................................... 468
Cumulative Review Exercises (Chapters 1−4) ...................................................... 469
Chapter 5 Analytic Trigonometry
5.1 Trigonometric Identities ........................................................................... 472
5.2 Sum and Difference Formulas .................................................................. 486
5.3 Double-Angle and Half-Angle Formulas ................................................. 500
5.4 Product-to-Sum and Sum-to-Product Formulas ....................................... 516
5.5 Trigonometric Equations I........................................................................ 525
5.6 Trigonometric Equations II ...................................................................... 535
Chapter 5 Key Ideas at a Glance ........................................................................... 555
Chapter 5 Review Exercises .................................................................................. 556
Chapter 5 Practice Test A ...................................................................................... 562
Chapter 5 Practice Test B ...................................................................................... 564
Cumulative Review Exercises (Chapters 1−5) ...................................................... 565
Chapter 6 Applications of Trigonometric Functions
6.1 Right-Triangle Trigonometry ................................................................... 568
6.2 The Law of Sines...................................................................................... 577
6.3 The Law of Cosines.................................................................................. 593
6.4 Vectors ..................................................................................................... 608
6.5 The Dot Product ....................................................................................... 617
6.6 Polar Coordinates ..................................................................................... 627
6.7 Polar Form of Complex Numbers; DeMoivre’s Theorem ....................... 646
Chapter 6 Key Ideas at a Glance ........................................................................... 660
Chapter 6 Review Exercises .................................................................................. 661
Chapter 6 Practice Test A ...................................................................................... 670
Chapter 6 Practice Test B ...................................................................................... 671
Cumulative Review Exercises (Chapters 1−6) ...................................................... 673
Chapter 7 Systems of Equations and Inequalities
7.1 Systems of Equations in Two Variables................................................... 676
7.2 Systems of Linear Equations in Three Variables ..................................... 699
7.3 Systems of Inequalities............................................................................. 724
7.4 Matrices and Systems of Equations.......................................................... 746
7.5 Determinants and Cramer’s Rule ............................................................. 768
7.6 Partial-Fraction Decomposition ............................................................... 780
7.7 Matrix Algebra ......................................................................................... 804
7.8 The Matrix Inverse ................................................................................... 824
Chapter 7 Key Ideas at a Glance ........................................................................... 844
Chapter 7 Review Exercises .................................................................................. 847
Chapter 7 Practice Test A ...................................................................................... 863
Chapter 7 Practice Test B ...................................................................................... 865
Cumulative Review Exercises (Chapters 1−7) ...................................................... 868
Chapter 8 Analytic Geometry
8.2 The Parabola ............................................................................................. 871
8.3 The Ellipse................................................................................................ 886
8.4 The Hyperbola .......................................................................................... 905
8.5 Rotation of Axes....................................................................................... 929
8.6 Polar Equations of Conics ........................................................................ 948
8.7 Parametric Equations................................................................................ 959
Copyright © 2023 Pearson Education Inc.
MANUAL
BEVERLY FUSFIELD
PRECALCULUS
A U NIT C IRCLE A PPROACH
FOURTH EDITION
J. S. Ratti
Marcus McWaters
Leslaw A. Skrzypek
with
Jessica Bernards
Wendy Fresh
, CONTENTS
Chapter 1 Graphs and Functions
1.1 The Coordinate Plane ................................................................................... 1
1.2 Graphs of Equations ................................................................................... 11
1.3 Lines ........................................................................................................... 24
1.4 Functions .................................................................................................... 39
1.5 Properties of Functions............................................................................... 49
1.6 A Library of Functions ............................................................................... 59
1.7 Transformations of Functions .................................................................... 71
1.8 Combining Functions; Composite Functions ............................................. 88
1.9 Inverse Functions ..................................................................................... 109
Chapter 1 Key Ideas at a Glance ........................................................................... 125
Chapter 1 Review Exercises .................................................................................. 127
Chapter 1 Practice Test A ...................................................................................... 138
Chapter 1 Practice Test B ...................................................................................... 140
Chapter 2 Polynomial and Rational Functions
2.1 Quadratic Functions ................................................................................. 141
2.2 Polynomial Functions ............................................................................... 163
2.3 Dividing Polynomials and the Rational Zeros Test .................................. 180
2.4 Rational Functions.................................................................................... 203
2.5 Polynomial and Rational Inequalities....................................................... 230
2.6 Zeros of a Polynomial Function ............................................................... 260
2.7 Variation ................................................................................................... 273
Chapter 2 Key Ideas at a Glance ........................................................................... 278
Chapter 2 Review Exercises .................................................................................. 281
Chapter 2 Practice Test A ...................................................................................... 298
Chapter 2 Practice Test B ...................................................................................... 299
Cumulative Review Exercises (Chapters 1−2) ...................................................... 301
Chapter 3 Exponential and Logarithmic Functions
3.1 Exponential Functions .............................................................................. 305
3.2 Logarithmic Functions ............................................................................. 318
3.3 Rules of Logarithms ................................................................................. 332
3.4 Exponential and Logarithmic Equations and Inequalities ........................ 344
3.5 Logarithmic Scales; Modeling ................................................................. 359
Chapter 3 Key Ideas at a Glance ........................................................................... 370
Chapter 3 Review Exercises .................................................................................. 370
Chapter 3 Practice Test A ...................................................................................... 379
Chapter 3 Practice Test B ...................................................................................... 380
Cumulative Review Exercises (Chapters 1−3) ...................................................... 381
Chapter 4 Trigonometric Functions
4.1 Angles and Their Measure ....................................................................... 385
4.2 The Unit Circle; Trigonometric Functions of Real Numbers ................... 392
4.3 Trigonometric Functions of Angles ......................................................... 406
4.4 Graphs of the Sine and Cosine Functions................................................. 418
4.5 Graphs of the Other Trigonometric Functions ......................................... 437
4.6 Inverse Trigonometric Functions ............................................................. 452
Chapter 4 Key Ideas at a Glance ........................................................................... 461
Chapter 4 Review Exercises .................................................................................. 463
Copyright © 2023 Pearson Education Inc.
, Chapter 4 Practice Test A ...................................................................................... 467
Chapter 4 Practice Test B ...................................................................................... 468
Cumulative Review Exercises (Chapters 1−4) ...................................................... 469
Chapter 5 Analytic Trigonometry
5.1 Trigonometric Identities ........................................................................... 472
5.2 Sum and Difference Formulas .................................................................. 486
5.3 Double-Angle and Half-Angle Formulas ................................................. 500
5.4 Product-to-Sum and Sum-to-Product Formulas ....................................... 516
5.5 Trigonometric Equations I........................................................................ 525
5.6 Trigonometric Equations II ...................................................................... 535
Chapter 5 Key Ideas at a Glance ........................................................................... 555
Chapter 5 Review Exercises .................................................................................. 556
Chapter 5 Practice Test A ...................................................................................... 562
Chapter 5 Practice Test B ...................................................................................... 564
Cumulative Review Exercises (Chapters 1−5) ...................................................... 565
Chapter 6 Applications of Trigonometric Functions
6.1 Right-Triangle Trigonometry ................................................................... 568
6.2 The Law of Sines...................................................................................... 577
6.3 The Law of Cosines.................................................................................. 593
6.4 Vectors ..................................................................................................... 608
6.5 The Dot Product ....................................................................................... 617
6.6 Polar Coordinates ..................................................................................... 627
6.7 Polar Form of Complex Numbers; DeMoivre’s Theorem ....................... 646
Chapter 6 Key Ideas at a Glance ........................................................................... 660
Chapter 6 Review Exercises .................................................................................. 661
Chapter 6 Practice Test A ...................................................................................... 670
Chapter 6 Practice Test B ...................................................................................... 671
Cumulative Review Exercises (Chapters 1−6) ...................................................... 673
Chapter 7 Systems of Equations and Inequalities
7.1 Systems of Equations in Two Variables................................................... 676
7.2 Systems of Linear Equations in Three Variables ..................................... 699
7.3 Systems of Inequalities............................................................................. 724
7.4 Matrices and Systems of Equations.......................................................... 746
7.5 Determinants and Cramer’s Rule ............................................................. 768
7.6 Partial-Fraction Decomposition ............................................................... 780
7.7 Matrix Algebra ......................................................................................... 804
7.8 The Matrix Inverse ................................................................................... 824
Chapter 7 Key Ideas at a Glance ........................................................................... 844
Chapter 7 Review Exercises .................................................................................. 847
Chapter 7 Practice Test A ...................................................................................... 863
Chapter 7 Practice Test B ...................................................................................... 865
Cumulative Review Exercises (Chapters 1−7) ...................................................... 868
Chapter 8 Analytic Geometry
8.2 The Parabola ............................................................................................. 871
8.3 The Ellipse................................................................................................ 886
8.4 The Hyperbola .......................................................................................... 905
8.5 Rotation of Axes....................................................................................... 929
8.6 Polar Equations of Conics ........................................................................ 948
8.7 Parametric Equations................................................................................ 959
Copyright © 2023 Pearson Education Inc.
