Algebra and Trigonometry Enhanced with Graphing Utilities

Algebra and Trigonometry Enhanced with Graphing Utilities, 8th edition

  • Michael Sullivan

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Algebra and Trigonometry Enhanced with Graphing Utilities takes a practical approach to integrating graphing tools and techniques into an exploration of advanced math concepts.

Published by Pearson (September 1st 2020) - Copyright © 2021

ISBN-13: 9780136872795

Subject: Precalculus, College Algebra & Trigonometry

Category: Algebra & Trigonometry

Table of contents

R. Review
R.1 Real Numbers
R.2 Algebra Essentials
R.3 Geometry Essentials
R.4 Polynomials
R.5 Factoring Polynomials
R.6 Synthetic Division
R.7 Rational Expressions
R.8 n th Roots; Rational Exponents

1. Graphs, Equations, and Inequalities
1.1 Graphing Utilities; Introduction to Graphing Equations
1.2 Solving Equations Using a Graphing Utility; Linear and Rational Equations
1.3 Quadratic Equations
1.4 Complex Numbers; Quadratic Equations in the Complex Number System
1.5 Radical Equations; Equations Quadratic in Form; Absolute Value Equations; Factorable Equations
1.6 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
1.7 Solving Inequalities

2. Graphs
2.1 The Distance and Midpoint Formulas
2.2 Intercepts: Symmetry; Graphing Key Equations
2.3 Lines
2.4 Circles
2.5 Variation

3. Functions and Their Graphs
3.1 Functions
3.2 The Graph of a Function
3.3 Properties of Functions
3.4 Library of Functions; Piecewise-defined Functions
3.5 Graphing Techniques: Transformations
3.6 Mathematical Models: Building Functions

4. Linear and Quadratic Functions
4.1 Properties of Linear Functions and Linear Models
4.2 Building Linear Models from Data
4.3 Quadratic Functions and Their Properties
4.4 Build Quadratic Models from Verbal Descriptions and from Data
4.5 Inequalities Involving Quadratic Functions

5. Polynomial and Rational Functions
5.1 Polynomial Functions
5.2 The Graph of a Polynomial Function; Models
5.3 The Real Zeroes of a Polynomial Function
5.4 Complex Zeroes: Fundamental Theorem of Algebra
5.5 Properties of Rational Functions
5.6 The Graph of a Rational Function
5.7 Polynomial and Rational Inequalities

6. Exponential and Logarithmic Functions
6.1 Composite Functions
6.2 One-to-One Functions; Inverse Functions
6.3 Exponential Functions
6.4 Logarithmic Functions
6.5 Properties of Logarithms
6.6 Logarithmic and Exponential Equations
6.7 Financial Models
6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
6.9 Building Exponential, Logarithmic, and Logistic Models from Data

7. Trigonometric Functions
7.1 Angles and Their Measure
7.2 Right Triangle Trigonometry
7.3 Computing the Values of Trigonometric Functions of Acute Angles
7.4 Trigonometric Functions of Any Angle
7.5 Unit Circle Approach; Properties of the Trigonometric Functions
7.6 Graphs of the Sine and Cosine Functions
7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
7.8 Phase Shift; Sinusoidal Curve Fitting

8. Analytic Trigonometry
8.1 The Inverse Sine, Cosine, and Tangent Functions
8.2 The Inverse Trigonometric Functions (Continued)
8.3 Trigonometric Equations
8.4 Trigonometric Identities
8.5 Sum and Difference Formulas
8.6 Double-angle and Half-angle Formulas
8.7 Product-to-Sum and Sum-to-Product Formulas

9. Applications of Trigonometric Functions
9.1 Applications Involving Right Triangles
9.2 The Law of Sines
9.3 The Law of Cosines
9.4 Area of a Triangle
9.5 Simple Harmonic Motion; Damped Motion; Combining Waves

10. Polar Coordinates; Vectors
10.1 Polar Coordinates
10.2 Polar Equations and Graphs
10.3 The Complex Plane; De Moivre’s Theorem
10.4 Vectors
10.5 The Dot Product

11. Analytic Geometry
11.1 Conics
11.2 The Parabola
11.3 The Ellipse
11.4 The Hyperbola
11.5 Rotation of Axes; General Form of a Conic
11.6 Polar Equations of Conics
11.7 Plane Curves and Parametric Equations

12. Systems of Equations and Inequalities
12.1 Systems of Linear Equations: Substitution and Elimination
12.2 Systems of Linear Equations: Matrices
12.3 Systems of Linear Equations: Determinants
12.4 Matrix Algebra
12.5 Partial Fraction Decomposition
12.6 Systems of Nonlinear Equations
12.7 Systems of Inequalities
12.8 Linear Programming

13. Sequences; Induction; the Binomial Theorem
13.1 Sequences
13.2 Arithmetic Sequences
13.3 Geometric Sequences; Geometric Series
13.4 Mathematical Induction
13.5 The Binomial Theorem

14. Counting and Probability
14.1 Counting
14.2 Permutations and Combinations
14.3 Probability

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