## Algebra and Trigonometry: Graphing and Data Analysis, 1/e

Michael Sullivan, Chicago State University
Michael Sullivan, South Suburban College

Published December, 1997 by Prentice Hall Engineering/Science/Mathematics

Cloth
ISBN 0-13-778481-3

mailings
on this subject.

Algebra/Trig with Graphing Calculators-Mathematics

Designed for the Precalculus course covering Algebra and Trigonometry. This text covers right angle trigonometry first and then develops the unit circle approach. This text requires student use of graphing calculators or a computer based software program. For schools who wish to cover unit circle first, please see “Precalculus: Graphing and Data Analysis”.
The goal of this text is to provide a solid mathematical foundation via visualization of real world data. Technology is used as a tool to solve problems, motivate concepts, explore and preview mathematical concepts and to find curves of best fit to the data. Most mathematical concepts are developed and illustrated both algebraically and graphically - with the more intuitive and appropriate method presented first.

@BREAKNOLINALT = Mathematics
The authors use their extensive teaching and writing experiences to guide and support students through the typical difficult areas.
Each section opens with the mathematical objectives of the section. Each objective is referenced as it is encountered in the section.
Examples are worked out step-by-step, both numerically and in “English”.
Many examples include the “Now Work” feature which suggests a similar odd-numbered problem from the section exercise set. This allows for immediate reinforcement of concepts through doing.
“Historical Notes” are provided in context, enhancing student interest, provide anecdotal information on how and where mathematical concepts have come from.
Exercises are carefully crafted — beginning with confidence builders and visualization exercises, then practice and drill, followed by the more challenging and application driven problems. Discussion, Writing and Research questions are clearly called out by the red icon in the margin.
Each chapter opens by listing the concepts (and page references) that the student will need to review “Before Getting Started”.
The chapters conclude with a detailed chapter review, including “Important Formulas, Theorems and Definitions”, a list of “Things to Know and Do”, True/False Questions, Fill-in-the-Blank items, and Review Exercises. @BREAKNOLINALT = Technology
The authors approach the use of technology as an enhancement to the learning of mathematics not as a replacement for learning.
Graphing utilities are used to help students analyze data and find curves of best fit. Types of curve fitting discussed include: linear, quadratic, cubic, power, exponential, logarithmic, logistic, and sinusoidal.
Using the power of the grapher, students are able to approach problems and concepts that may have been beyond them without the grapher.
Real TI-83 screen shots are used as the illustrations for the purpose of clear visualization of the materials. @BREAKNOLINALT = Data
Sourced data connects the mathematical concepts to other disciplines and other interests of the students - adding relevancy and motivation.
Applications involving data analysis utilize real world sources such as the US Census Bureau, Government Agencies and the Internet.
Each chapter has an “Internet Exploration”. These optional explorations introduce students to “live data” via the Internet. Multiple questions follow each exploration encouraging the use of Polya's problem solving strategies. The links to the sites are all maintained via the Prentice Hall Companion Website for Sullivan at
www.prenhall.com/sullivan

(NOTE: Chapters end with Chapter Review.)

1. Graphs.

Data and its Representation. Rectangular Coordinates; Graphing Utilities; Data in Ordered Pairs. Graphs of Equations. Lines. Parallel and Perpendicular Lines; Circles. Linear Curve Fitting. Variation.

2. Functions and Their Graphs.

Functions. More About Functions. Graphing Techniques. Operations on Functions; Composite Functions. Mathematical Models: Constructing Functions.

3. Equations and Inequalities.

Solving Equations Using A Graphing Utility. Linear and Quadratic Equations. Setting Up Equations: Applications. Other Types of Equations. Inequalities. Equations and Inequalities Involving Absolute Value.

4. Polynomial and Rational Functions.

Quadratic Functions; Curve Fitting. Power Functions; Curve Fitting. Polynomial Functions; Curve Fitting. Rational Functions. The Real Zeros of a Polynomial Function. Complex Numbers; Quadratic Equations with a Negative Discriminant. Complex Zeros; Fundamental Theorem of Algebra. Polynomial and Rational Inequalities.

5. Exponential and Logarithmic Functions.

One-to-One Functions; Inverse Functions. Exponential Functions. Logarithmic Functions. Properties of Logarithms. Logarithmic and Exponential Equations. Compound Interest. Growth and Decay. Exponential, Logarithmic, and Logistic Curve Fitting. Logarithmic Scales.

6. Trigonometric Functions.

Angles and Their Measure. Right Triangle Trigonometry. Computing the Values of Trigonometric Functions of Given Angles. Trigonometric Functions of a General Angle. Properties of the Trigonometric Functions. Graphs of the Trigonometric Functions. The Inverse Trigonometric Functions.

7. Analytic Trigonometry.

Trigonometric Identities. Sum and Difference Formulas. Double-Angle and Half-Angle Formulas. Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations.

8. Applications of Trigonometric Functions.

Solving Right Triangles. The Law of Sines. The Law of Cosines. The Area of a Triangle. Sinusoidal Graphs: Sinusoidal Curve Fitting. Simple Harmonic Motion: Damped Motion.

9. Polar Coordinates; Vectors.

Polar Coordinates. Polar Equations and Graphs. The Complex Plane; Demoivre's Theorem. Vectors. The Dot Product.

10. Analytic Geometry.

Conics. The Parabola. The Ellipse. The Hyperbola. Rotation of Axes; General Form of a Conic. Polar Equations of Conics. Plane Curves and Parametric Equations.

11. Systems of Equations and Inequalities.

Systems of Linear Equations: Substitution; Elimination. Systems of Linear Equations; Matrices. Systems of Linear Equations: Determinants. Matrix Algebra. Partial Fraction Decomposition. Systems of Nonlinear Equations. Systems of Inequalities. Linear Programming.

12. Sequences; Induction; Counting; Probability.

Sequences. Arithmetic Sequences. Geometric Sequences; Geometric Series. Mathematical Induction. The Binomial Theorem. Sets and Counting Permutations and Combinations. Probability.

Appendix Review:

Topics from Algebra and Geometry. Polynomials and Rational Expressions. Radicals; Rational Exponents. Solving Equations. Completing the Square. Synthetic Division.