Solutions Manual for Algebra and Trigonometry, 12th Edition by Michael Sullivan

SOLUTIONS MANUAL l




TIM BRITT
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ALGEBRA AND l




l T RIGONOMETRY
l TWELFTHEDITION l




MichaelSullivan
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, Table of Contents
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Chapter R l Review
R.1 Real Numbers............................................................................................................................ 1
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R.2 Algebra Essentials ..................................................................................................................... 5
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R.3 Geometry Essentials ................................................................................................................ 11
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R.4 Polynomials ............................................................................................................................ 16
R.5 Factoring Polynomials............................................................................................................. 23
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R.6 Synthetic Division ................................................................................................................... 28
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R.7 Rational Expressions ............................................................................................................... 30
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R.8 nth Roots; Rational Exponents ................................................................................................. 40
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Chapter 1 l Equations and Inequalities l l




1.1 Linear Equations ...................................................................................................................... 50
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1.2 Quadratic Equations ................................................................................................................. 68
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1.3 Complex Numbers; Quadratic Equations in the Complex Number System ................................ 86
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1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations ................................... 92
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1.5 Solving Inequalities ............................................................................................................... 116
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1.6 Equations and Inequalities Involving Absolute Value ............................................................. 127
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1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications ........... 137
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Chapter Review ............................................................................................................................ 145
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Chapter Test.................................................................................................................................. 153
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Chapter Projects ............................................................................................................................ 155
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Chapter 2 l Graphs
2.1 The Distance and Midpoint Formulas ..................................................................................... 156
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2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry ................................................. 169
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2.3 Lines ...................................................................................................................................... 183
2.4 Circles ................................................................................................................................... 201
2.5 Variation................................................................................................................................ 215
Chapter Review ............................................................................................................................ 221
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Chapter Test.................................................................................................................................. 227
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Cumulative Review....................................................................................................................... 229
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Chapter Project ............................................................................................................................. 231
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Chapter 3 l Functions and Their Graphs l l l




3.1 Functions ............................................................................................................................... 232
3.2 The Graph of a Function ......................................................................................................... 250
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3.3 Properties of Functions........................................................................................................... 259
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3.4 Library of Functions; Piecewise-defined Functions ................................................................ 276
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3.5 Graphing Techniques: Transformations ................................................................................. 288
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3.6 Mathematical Models: Building Functions ............................................................................. 306
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Chapter Review ............................................................................................................................ 314
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Chapter Test.................................................................................................................................. 321
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Cumulative Review ...................................................................................................................... 324
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Chapter Projects............................................................................................................................ 328
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,Chapter 4 l Linear and Quadratic Functions l l l




4.1 Properties of Linear Functions and Linear Models .................................................................. 330
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4.2 Building Linear Functions from Data...................................................................................... 341
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4.3 Quadratic Functions and Their Properties ............................................................................... 347
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4.4 Build Quadratic Models from Verbal Descriptions and from Data ........................................... 371
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4.5 Inequalities Involving Quadratic Functions ............................................................................ 378
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Chapter Review ............................................................................................................................ 398
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Chapter Test.................................................................................................................................. 406
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Cumulative Review....................................................................................................................... 408
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Chapter Projects ............................................................................................................................ 411
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Chapter 5 l Polynomial and Rational Functions l l l




5.1 Polynomial Functions ............................................................................................................ 414
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5.2 Graphing Polynomial Functions; Models ................................................................................ 424
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5.3 Properties of Rational Functions ............................................................................................. 440
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5.4 The Graph of a Rational Function ........................................................................................... 450
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5.5 Polynomial and Rational Inequalities ..................................................................................... 506
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5.6 The Real Zeros of a Polynomial Function ................................................................................ 527
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5.7 Complex Zeros; Fundamental Theorem of Algebra................................................................. 558
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Chapter Review ............................................................................................................................ 567
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Chapter Test.................................................................................................................................. 582
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Cumulative Review....................................................................................................................... 586
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Chapter Projects ............................................................................................................................ 591
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Chapter 6 l Exponential and Logarithmic Functions l l l




6.1 Composite Functions ............................................................................................................. 593
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6.2 One-to-One Functions; Inverse Functions .............................................................................. 611
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6.3 Exponential Functions ........................................................................................................... 634
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6.4 Logarithmic Functions ........................................................................................................... 655
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6.5 Properties of Logarithms ........................................................................................................ 677
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6.6 Logarithmic and Exponential Equations ................................................................................. 686
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6.7 Financial Models.................................................................................................................... 707
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6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth
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and Decay Models ............................................................................................................... 715
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6.9 Building Exponential, Logarithmic, and Logistic Models from Data ....................................... 725
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Chapter Review ............................................................................................................................ 729
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Chapter Test.................................................................................................................................. 742
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Cumulative Review....................................................................................................................... 746
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Chapter Projects ............................................................................................................................ 749
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, Chapter 7 l Trigonometric Functions l




7.1 Angles, Arc Length, and Circular Motion ....................................................................................752
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7.2 Right Triangle Trigonometry ................................................................................................. 761
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7.3 Computing the Values of Trigonometric Functions of Acute Angles ....................................... 777
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7.4 Trigonometric Functions of Any Angle .................................................................................. 790
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7.5 Unit Circle Approach: Properties of the Trigonometric Functions ..............................................806
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7.6 Graphs of the Sine and Cosine Functions................................................................................. 815
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7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions ........................................ 837
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7.8 Phase Shift; Sinusoidal Curve Fitting...................................................................................... 847
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Chapter Review ............................................................................................................................ 860
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Chapter Test.................................................................................................................................. 869
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Cumulative Review....................................................................................................................... 873
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Chapter Projects ............................................................................................................................ 877
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Chapter 8 l Analytic Trigonometry l




8.1 The Inverse Sine, Cosine, and Tangent Functions ................................................................... 881
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8.2 The Inverse Trigonometric Functions (Continued) ................................................................. 895
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8.3 Trigonometric Equations ....................................................................................................... 907
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8.4 Trigonometric Identities......................................................................................................... 928
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8.5 Sum and Difference Formulas ................................................................................................ 941
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8.6 Double-angle and Half-angle Formulas .................................................................................. 966
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8.7 Product-to-Sum and Sum-to-Product Formulas ..........................................................................994
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Chapter Review ...........................................................................................................................1007
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Chapter Test.................................................................................................................................1022
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Cumulative Review......................................................................................................................1027
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Chapter Projects ...........................................................................................................................1033
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Chapter 9 l Applications of Trigonometric Functions l l l




9.1 Applications Involving Right Triangles .................................................................................1037
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9.2 The Law of Sines ...................................................................................................................1045
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9.3 The Law of Cosines ...............................................................................................................1060
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9.4 Area of a Triangle ..................................................................................................................1072
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9.5 Simple Harmonic Motion; Damped Motion; Combining Waves ............................................1082
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Chapter Review ...........................................................................................................................1092
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Chapter Test.................................................................................................................................1098
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Cumulative Review......................................................................................................................1101
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Chapter Projects ...........................................................................................................................1107
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Chapter 10 l Polar Coordinates; Vectors l l




10.1 Polar Coordinates................................................................................................................1111
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10.2 Polar Equations and Graphs .................................................................................................1120
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10.3 The Complex Plane; De Moivre’s Theorem .........................................................................1149
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10.4 Vectors ...............................................................................................................................1163
10.5 The Dot Product ..................................................................................................................1176
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Chapter Review ...........................................................................................................................1182
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Chapter Test.................................................................................................................................1190
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Cumulative Review......................................................................................................................1194
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Chapter Projects ...........................................................................................................................1196
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