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Summary: This book introduces trigonometry through the unit circle. Cohen emphasizes graphing to explain complex concepts in an uncomplicated style, and provides supplementary graphing-calculator exercises at the end of most sections for additional perspective and reinforcement.Edition/Copyright: 3RD 98
PART I. ALGEBRA BACKGROUND FOR PRECALCULUS.
Sets of Real Numbers.
Polynomials and Factoring.
PART II. COORDINATES, GRAPHS, AND INEQUALITIES.
Graphs and Equations, A Second Look.
Equations of Lines.
Symmetry and Graphs.
More on Inequalities.
PART III. FUNCTIONS.
The Definition of a Function.
The Graph of a Function.
Techniques in Graphing.
Methods of Combining Functions.
Iteration. Inverse Functions.
PART IV. POLYNOMIAL AND RATIONAL FUNCTIONS.
Applications to Iterations and Optimization.
More on Iteration.
Quadratics and Population Growth.
Applied Functions : Setting Up Equations.
Maximum and Minimum Problems.
PART V. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
The Exponential Function y = e to the x Power.
Properties of Logarithms.
Equations and Inequalities with Logs and Exponents.
Exponential Growth and Decay.
PART VI. THE TRIGONOMETRIC FUNCTIONS.
Trigonometric Functions of Angles.
Evaluating the Trigonometric Functions.
Algebra and the Trigonometric Functions.
PART VII. GRAPHS OF THE TRIGONOMETRIC FUNCTIONS.
Trigonometric Functions of Real Numbers.
Graphs of the Sine and the Cosine Functions.
Graphs of y = A sin(Bx-C) and y = A cos(Bx - C).
Simple Harmonic Motion.
Graphs of the Tangent and the Reciprocal Functions.
PART VIII. ANALYTICAL TRIGONOMETRY.
The Addition Formulas.
The Double-Angle Formulas.
The Product-to-Sum and Sum-to-Product Formulas.
The Inverse Trigonometric Functions.
PART IX. ADDITIONAL TOPICS IN TRIGONOMETRY.
The Law of Sines and the Law of Cosines.
Vectors in the Plane, a Geometric Approach.
Vectors in the Plane, an Algebraic Approach.
Introduction to Polar Coordinates.
Curves in Polar Coordinates.
PART X. SYSTEMS OF EQUATIONS.
Systems of Two Linear Equations in Two Unknowns.
The Inverse of a Square Matrix.
Determinants and Cramer's Rule.
Nonlinear Systems of Equations.
Systems of Inequalities.
PART XI. ANALYTIC GEOMETRY.
The Basic Equations.
Tangents to Parabolas (Optional).
The Focus-Directrix Property of Conics.
The Conics in Polar Coordinates.
Rotation of Axes.
PART XII. ROOTS OF POLYNOMIAL EQUATIONS.
The Complex Number System.
Division of Polynomials.
Roots of Polynomial Equations : The Remainder Theorem and the Factor Theorem.
The Fundamental Theorem of Algebra.
Rational and Irrational Roots.
Conjugate Roots and Descartes' Rule of Signs.
Introduction to Partial Fractions.
More About Partial Fractions.
PART XIII. ADDITIONAL TOPICS.
The Binomial Theorem.
Introduction to Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
Appendix A.1 : Using a Graphing Utility.
Appendix A.2 : Significant Digits and Calculators.
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