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
Copyright 1998, 1137 pp.
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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
Examples are worked out step-by-step, both numerically and
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
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,
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
Applications involving data analysis utilize real world
sources such as the US Census Bureau, Government Agencies and the
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
(NOTE: Chapters end with Chapter Review.)
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
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.
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.
Topics from Algebra and Geometry. Polynomials and Rational
Expressions. Radicals; Rational Exponents. Solving Equations. Completing
the Square. Synthetic Division.