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Connally E. et al - Functions modelling change (2011)




pages :  674
File Type :  PDF
Contents  :   LINEAR FUNCTIONS AND CHANGE, FUNCTIONS, QUADRATIC FUNCTIONS, EXPONENTIAL FUNCTIONS, : EXPONENTS , LOGARITHMIC FUNCTIONS, TRANSFORMATIONS OF FUNCTIONS AND THEIR GRAPHS, TRIGONOMETRY IN CIRCLES AND TRIANGLES ,  THE TRIGONOMETRIC FUNCTIONS , TRIGONOMETRIC IDENTITIES AND THEIR APPLICATIONS  ,   COMPOSITIONS, INVERSES, AND COMBINATIONS OF FUNCTIONS   ,  POLYNOMIAL AND RATIONAL FUNCTIONS  ,     VECTORS AND MATRICES  ,  SEQUENCES AND SERIES  ,  PARAMETRIC EQUATIONS AND CONIC SECTIONS  ,  ANSWERS TO ODD-NUMBERED PROBLEMS

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 Demana F. D. et al - Precalculus (2011)




Franklin D. Demana
Bert K. Waits
Gregory D. Foley
Daniel Kennedy

pages  :  1026
file Type  :  Pdf

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Contents  :

Prerequisites
P.1 Real Numbers  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Representing Real Numbers ~ Order and Interval Notation ~ Basic
Properties of Algebra ~ Integer Exponents ~ Scientific Notation
P.2 Cartesian Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . 12
Cartesian Plane ~ Absolute Value of a Real Number ~ Distance
Formulas ~ Midpoint Formulas ~ Equations of Circles ~ Applications
P.3 Linear Equations and Inequalities  . . . . . . . . . . . . . . . . . . . 21
Equations ~ Solving Equations ~ Linear Equations in One Variable ~
Linear Inequalities in One Variable
P.4 Lines in the Plane  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Slope of a Line ~ Point-Slope Form Equation of a Line ~ Slope-
Intercept Form Equation of a Line ~ Graphing Linear Equations in
Two Variables ~ Parallel and Perpendicular Lines ~ Applying Linear
Equations in Two Variables
P.5 Solving Equations Graphically,
Numerically, and Algebraically  . . . . . . . . . . . . . . . . . . . . . . 40
Solving Equations Graphically ~ Solving Quadratic Equations ~
Approximating Solutions of Equations Graphically ~ Approximating
Solutions of Equations Numerically with Tables ~ Solving Equations
by Finding Intersections
P.6 Complex Numbers  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
Complex Numbers ~ Operations with Complex Numbers ~ Complex
Conjugates and Division ~ Complex Solutions of Quadratic Equations
P.7 Solving Inequalities Algebraically and Graphically  . . . . . 54
Solving Absolute Value Inequalities ~ Solving Quadratic Inequalities ~
Approximating Solutions to Inequalities ~ Projectile Motion
Key Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Review Exercises  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Functions and Graphs
1.1 Modeling and Equation Solving . . . . . . . . . . . . . . . . . . . . . . .64
Numerical Models ~ Algebraic Models ~ Graphical Models ~ The Zero
Factor Property ~ Problem Solving ~ Grapher Failure and Hidden
Behavior ~ A Word About Proof
1.2 Functions and Their Properties  . . . . . . . . . . . . . . . . . . . . . 80
Function Definition and Notation ~ Domain and Range ~ Continuity
~ Increasing and Decreasing Functions ~ Boundedness ~ Local and
Absolute Extrema ~ Symmetry ~ Asymptotes ~ End Behavior
1.3 Twelve Basic Funct ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
What Graphs Can Tell Us ~ Twelve Basic Funct ions ~ Analyzing
Functions Graphically
1.4 Building Functions from Functions  . . . . . . . . . . . . . . . . . 110
Combining Functions Algebraically ~ Composition of Functions ~
Relations and Implicitly Defined Functions
1.5 Parametric Relations and Inverses  . . . . . . . . . . . . . . . . . . 119
Relations Defined Parametrically ~ Inverse Relations and Inverse
Functions
1.6 Graphical Transformations . . . . . . . . . . . . . . . . . . . . . . . . . 129
Transformations ~ Ve r t i c a l and Hor i zont a l Tr ans l a t ions ~
Reflections Across Axes ~ Ve r t i c a l and Hor i zont a l St r e t che s and
Shrinks ~ Combining Transformations
1.7 Modeling with Functions  . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Functions from Formulas ~ Functions from Graphs ~ Functions
from Verbal Descriptions ~ Functions from Data
Key Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Review Exercises  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Chapter Project  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Polynomial, Power,
and Rational Functions
2.1 Linear and Quadratic Functions and Modeling  . . . . . . . 158
Polynomial Functions ~ Linear Functions and Their Graphs ~
Average Rate of Change ~ Linear Correlation and Modeling ~
Quadratic Functions and Their Graphs ~ Applications
of Quadratic Functions
2.2 Power Functions with Modeling  . . . . . . . . . . . . . . . . . . . . 174
Power Functions and Variation ~ Monomial Functions and
Their Graphs ~ Graphs of Power Functions ~ Modeling with
Power Functions
2.3 Polynomial Functions of
Higher Degree with Modeling  . . . . . . . . . . . . . . . . . . . . . . 185
Graphs of Polynomial Functions ~ End Behavior of Polynomial
Functions ~ Zeros of Polynomial Functions ~ Intermediate Value
Theorem ~ Modeling
2.4 Real Zeros of Polynomial Functions  . . . . . . . . . . . . . . . . 197
Long Division and the Division Algorithm ~ Remainder and Factor
Theorems ~ Synthetic Division ~ Rational Zeros Theorem ~ Upper and
Lower Bounds
2.5 Complex Zeros and the
Fundamental Theorem of Algebra  . . . . . . . . . . . . . . . . . . 210
Two Major Theorems ~ Complex Conjugate Zeros ~ Factoring with
Real Number Coefficients
2.6 Graphs of Rational Functions  . . . . . . . . . . . . . . . . . . . . . . 218
Rational Functions ~ Transformations of the Reciprocal Function ~
Limits and Asymptotes ~ Analyzing Graphs of Rational Functions ~
Exploring Relative Humidity
2.7 Solving Equations in One Variable  . . . . . . . . . . . . . . . . . . 228
Solving Rational Equations ~ Extraneous Solutions ~ Applications
2.8 Solving Inequalities in One Variable . . . . . . . . . . . . . . . . . 236
Polynomial Inequalities ~ Rational Inequalities ~ Other Inequalities
~ Applications
Key Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
Review Exercises  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
Chapter Project  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
Exponential, Logistic,
and Logarithmic Functions
3.1 Exponential and Logistic Functions  . . . . . . . . . . . . . . . . . 252
Exponential Functions and Their Graphs ~ The Natural Base e ~
Logistic Functions and Their Graphs ~ Population Models
3.2 Exponential and Logistic Modeling . . . . . . . . . . . . . . . . . . 265
Constant Percentage Rate and Exponential Functions ~ Exponential
Growth and Decay Models ~ Using Regression to Model Population
~ Other Logistic Models
3.3 Logarithmic Functions and Their Graphs  . . . . . . . . . . . . 274
Inverses of Exponential Functions ~ Common Logarithms—Base 10
~ Natural Logarithms—Base e ~ Graphs of Logarithmic Functions ~
Measuring Sound Using Decibels
3.4 Properties of Logarithmic Functions  . . . . . . . . . . . . . . . . 283
Properties of Logarithms ~ Change of Base ~ Graphs of Logarithmic
Functions with Base b ~ Re-expressing Data
3.5 Equation Solving and Modeling . . . . . . . . . . . . . . . . . . . . . 292
Solving Exponential Equations ~ Solving Logarithmic Equations ~
Orders of Magnitude and Logarithmic Models ~ Newton’s Law of
Cooling ~ Logarithmic Re-expression
3.6 Mathematics of Finance  . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
Interest Compounded Annually ~ Interest Compounded k Times per
Year ~ Interest Compounded Continuously ~ Annual Percentage
Yield ~ Annuities—Future Value ~ Loans and Mortgages—Present Value
Key Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
Review Exercises  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
Chapter Project  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Trigonometric Functions
4.1 Angles and Their Measures  . . . . . . . . . . . . . . . . . . . . . . . . 320
The Problem of Angular Measure ~ Degrees and Radians ~ Circular
Arc Length ~ Angular and Linear Motion
4.2 Trigonometric Functions of Acute Angles  . . . . . . . . . . . . 329
Right Triangle Trigonometry ~ Two Famous Triangles ~ Evaluating
Trigonometric Functions with a Calculator ~ Common Calculator Errors When
Evaluating Trig Functions ~ Applications of Right Triangle Trigonometry
4.3 Trigonometry Extended: The Circular Functions  . . . . . 338
Trigonometric Functions of Any Angle ~ Trigonometric
Functions of Real Numbers ~ Periodic Functions ~ The 16-Point
Unit Circle
4.4 Graphs of Sine and Cosine: Sinusoids  . . . . . . . . . . . . . . . 350
The Basic Waves Revisited ~ Sinusoids and Transformations ~
Modeling Periodic Behavior with Sinusoids
4.5 Graphs of Tangent, Cotangent, Secant,
and Cosecant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
The Tangent Function ~ The Cotangent Function ~ The Secant
Function ~ The Cosecant Function
4.6 Graphs of Composite Trigonometric Functions  . . . . . . . 369
Combining Trigonometric and Algebraic Functions ~ Sums and
Differences of Sinusoids ~ Damped Oscillation
4.7 Inverse Trigonometric Functions  . . . . . . . . . . . . . . . . . . . 378
Inverse Sine Function ~ Inverse Cosine and Tangent Functions ~
Composing Trigonometric and Inverse Trigonometric Functions ~
Applications of Inverse Trigonometric Functions
4.8 Solving Problems with Trigonometry . . . . . . . . . . . . . . . . 388
More Right Triangle Problems ~ Simple Harmonic Motion
Key Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
Review Exercises  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
Chapter Project  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
Analytic Trigonometry
5.1 Fundamental Identities  . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404
Identities ~ Basic Trigonometric Identities ~ Pythagorean Identities
~ Cofunction Identities ~ Odd-Even Identities ~ Simplifying
Trigonometric Expressions ~ Solving Trigonometric Equations
5.2 Proving Trigonometric Identities  . . . . . . . . . . . . . . . . . . . 413
A Proof Strategy ~ Proving Identities ~ Disproving Non-Identities ~
Identities in Calculus
5.3 Sum and Difference Identities  . . . . . . . . . . . . . . . . . . . . . . 421
Cosine of a Difference ~ Cosine of a Sum ~ Sine of a Difference or
Sum ~ Tangent of a Difference or Sum ~ Ve r i fying a Sinusoid
Algebraically
5.4 Multiple-Angle Identities  . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
Double-Angle Identities ~ Power-Reducing Identities ~ Half-Angle
Identities ~ Solving Trigonometric Equations
5.5 The Law of Sines  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434
Deriving the Law of Sines ~ Solving Triangles (AAS, ASA) ~ The
Ambiguous Case (SSA) ~ Applications
5.6 The Law of Cosines  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
Deriving the Law of Cosines ~ Solving Triangles (SAS, SSS) ~
Triangle Area and Heron’s Formula ~ Applications
Key Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
Review Exercises  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
Chapter Project  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454
Applications of Trigonometry
6.1 Vectors in the Plane  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
Two-Dimensional Vectors ~ Ve c tor Ope r a t ions ~ Unit Vectors ~
Direction Angles ~ Applications of Vectors
6.2 Dot Product of Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467
The Dot Product ~ Angle Between Vectors ~ Projecting One Vector
onto Another ~ Work
6.3 Parametric Equations and Motion  . . . . . . . . . . . . . . . . . . 475
Parametric Equations ~ Parametric Curves ~ Eliminating the
Parameter ~ Lines and Line Segments ~ Simulating Motion with a
Grapher
6.4 Polar Coordinates  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
Polar Coordinate System ~ Coordinate Conversion ~ Equation
Conversion ~ Finding Distance Using Polar Coordinates
6.5 Graphs of Polar Equations  . . . . . . . . . . . . . . . . . . . . . . . . . 494
Polar Curves and Parametric Curves ~ Symmetry ~ Analyzing Polar
Graphs ~ Rose Curves ~ Limaçon Curves ~ Other Polar Curves
6.6 De Moivre’s Theorem and nth Roots  . . . . . . . . . . . . . . . . 503
The Complex Plane ~ Trigonometric Form of Complex Numbers ~
Multiplication and Division of Complex Numbers ~ Powers of
Complex Numbers ~ Roots of Complex Numbers
Key Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
Review Exercises  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514
Chapter Project  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517
Systems and Matrices
7.1 Solving Systems of Two Equations  . . . . . . . . . . . . . . . . . . 520
The Method of Substitution ~ Solving Systems Graphically ~
The Method of Elimination ~ Applications
7.2 Matrix Algebra  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
Matrices ~ Matrix Addition and Subtraction ~ Matrix Multiplication
~ Identity and Inverse Matrices ~ Determinant of a Square Matrix ~
Applications
7.3 Multivariate Linear Systems and Row Operations  . . . . . 544
Triangular Form for Linear Systems ~ Gaussian Elimination ~
Elementary Row Operations and Row Echelon Form ~ Reduced
Row Echelon Form ~ Solving Systems with Inverse Matrices ~
Applications
7.4 Partial Fractions  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557
Partial Fraction Decomposition ~ Denominators with Linear
Factors ~ Denominators with Irreducible Quadratic Factors ~
Applications
7.5 Systems of Inequalities in Two Variables  . . . . . . . . . . . . . 565
Graph of an Inequality ~ Systems of Inequalities ~ Linear Programming
Key Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573
Review Exercises  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573
Chapter Project  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 577
Analytic Geometry in
Two and Three Dimensions
8.1 Conic Sections and Parabolas  . . . . . . . . . . . . . . . . . . . . . . 580
Conic Sections ~ Geometry of a Parabola ~ Translations of
Parabolas ~ Reflective Property of a Parabola
8.2 Ellipses  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591
Geometry of an Ellipse ~ Translations of Ellipses ~ Orbits and
Eccentricity ~ Reflective Property of an Ellipse
8.3 Hyperbolas  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
Geometry of a Hyperbola ~ Translations of Hyperbolas ~ Eccentricity
and Orbits ~ Reflective Property of a Hyperbola ~ Long-Range
Navigation
8.4 Translation and Rotation of Axes  . . . . . . . . . . . . . . . . . . . 612
Second-Degree Equations in Two Variables ~ Translating Axes Versus
Translating Graphs ~ Rotation of Axes ~ Discriminant Test
8.5 Polar Equations of Conics  . . . . . . . . . . . . . . . . . . . . . . . . . 620
Eccentricity Revisited ~ Writing Polar Equations for Conics ~ Analyzing
Polar Equations of Conics ~ Orbits Revisited
8.6 Three-Dimensional Cartesian Coordinate System  . . . . . 629
Three-Dimensional Cartesian Coordinates ~ Distance and Midpoint
Formulas ~ Equation of a Sphere ~ Planes and Other Surfaces ~ Ve c tor s
in Space ~ Lines in Space
Key Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637
Review Exercises  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 638
Chapter Project  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640
Discrete Mathematics
9.1 Basic Combinatorics  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642
Discrete Versus Continuous ~ The Importance of Counting ~ The
Multiplication Principle of Counting ~ Permutations ~ Combinations ~
Subsets of an n-Set
9.2 The Binomial Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652
Powers of Binomials ~ Pascal’s Triangle ~ The Binomial Theorem ~
Factorial Identities
9.3 Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658
Sample Spaces and Probability Functions ~ Determining
Probabilities ~ Venn Di agr ams and Tr e e Di agr ams ~ Conditional
Probability ~ Binomial Distributions
9.4 Sequences  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 670
Infinite Sequences ~ Limits of Infinite Sequences ~ Arithmetic and
Geometric Sequences ~ Sequences and Graphing Calculators
9.5 Series  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 678
Summation Notation ~ Sums of Arithmetic and Geometric
Sequences ~ Infinite Series ~ Convergence of Geometric Series
9.6 Mathematical Induction  . . . . . . . . . . . . . . . . . . . . . . . . . . . 687
The Tower of Hanoi Problem ~ Principle of Mathematical Induction
~ Induction and Deduction
9.7 Statistics and Data (Graphical)  . . . . . . . . . . . . . . . . . . . . . 693
Statistics ~ Displaying Categorical Data ~ Stemplots ~ Frequency
Tables ~ Histograms ~ Time Plots
9.8 Statistics and Data (Algebraic)  . . . . . . . . . . . . . . . . . . . . . 704
Parameters and Statistics ~ Mean, Median, and Mode ~ The Five-
Number Summary ~ Boxplots ~ Va r i anc e and St anda rd Devi a t ion ~
Normal Distributions
9.9 Statistical Literacy  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717
The Many Misuses of Statistics ~ Correlation Revisited ~ The Importance
of Randomness ~ Surveys and Observational Studies ~ Experimental
Design ~ Using Randomness ~ Probability Simulations
Key Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 729
Review Exercises  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 729
Chapter Project  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733
An Introduction to Calculus:
Limits, Derivatives, and Integrals
10.1 Limits and Motion: The Tangent Problem  . . . . . . . . . . . 736
Average Veloci ty ~ Instantaneous Velocity ~ Limits Revisited ~
The Connection to Tangent Lines ~ The Derivative
10.2 Limits and Motion: The Area Problem  . . . . . . . . . . . . . . 747
Distance from a Constant Velocity ~ Distance from
a Changing Velocity ~ Limits at Infinity ~
The Connection to Areas ~ The Definite Integral
10.3 More on Limits  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755
A Little History ~ Defining a Limit Informally ~ Properties of Limits ~
Limits of Continuous Functions ~ One-Sided and Two-Sided Limits ~
Limits Involving Infinity
10.4 Numerical Derivatives and Integrals  . . . . . . . . . . . . . . . . 766
Derivatives on a Calculator ~ Definite Integrals on a Calculator ~
Computing a Derivative from Data ~ Computing a Definite Integral
from Data
Key Ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775
Review Exercises  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775
Chapter Project  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777
Algebra Review
A.1 Radicals and Rational Exponents  . . . . . . . . . . . . . . . . . . . 779
Radicals ~ Simplifying Radical Expressions ~ Rationalizing the
Denominator ~ Rational Exponents
A.2 Polynomials and Factoring . . . . . . . . . . . . . . . . . . . . . . . . . 784
Adding, Subtracting, and Multiplying Polynomials ~ Special
Products ~ Factoring Polynomials Using Special Products ~
Factoring Trinomials ~ Factoring by Grouping
A.3 Fractional Expressions  . . . . . . . . . . . . . . . . . . . . . . . . . . . . 791
Domain of an Algebraic Expression ~ Reducing Rational
Expressions ~ Operations with Rational Expressions ~
Compound Rational Expressions
Key Formulas
B.1 Formulas from Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796
Exponents ~ Radicals and Rational Exponents ~ Special Products
~ Factoring Polynomials ~ Inequalities ~ Quadratic Formula ~
Logarithms ~ Determinants ~ Arithmetic Sequences and Series ~
Geometric Sequences and Series ~ Factorial ~ Binomial Coefficient
~ Binomial Theorem
B.2 Formulas from Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . 797
Triangle ~ Trapezoid ~ Circle ~ Sector of Circle ~ Right Circular
Cone ~ Right Circular Cylinder ~ Right Triangle ~ Parallelogram ~
Circular Ring ~ Ellipse ~ Cone ~ Sphere
B.3 Formulas from Trigonometry  . . . . . . . . . . . . . . . . . . . . . . 797
Angular Measure ~ Reciprocal Identities ~ Quotient Identities ~
Pythagorean Identities ~ Odd-Even Identities ~ Sum and
Difference Identities ~ Cofunction Identities ~ Double-Angle
Identities ~ Power-Reducing Identities ~ Half-Angle Identities ~
Triangles ~ Trigonometric Form of a Complex Number ~
De Moivre’s Theorem
B.4 Formulas from Analytic Geometry  . . . . . . . . . . . . . . . . . . 799
Basic Formulas ~ Equations of a Line ~ Equation of a Circle ~
Parabolas with Vertex (h, k) ~ Ellipses with Center (h, k) and
a > b > 0 ~ Hyperbolas with Center (h, k)
B.5 Gallery of Basic Functions  . . . . . . . . . . . . . . . . . . . . . . . . . 800
Logic
C.1 Logic: An Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . 801
Statements ~ Compound Statements
C.2 Conditionals and Biconditionals  . . . . . . . . . . . . . . . . . . . . 807
Forms of Statements ~ Va l id Re a soning
Bibliography  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814
Glossary  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816
Selected Answers  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833
Applications Index  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935
Index  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 939

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