Precalculus Made Difficult

Front Matter
	Cover
	Title Page
	Copyright Page
	Table of Contents
	Preface for Teachers
	Changes in the 2nd Edition
	Preface for  Students
Part I: Algebra
	Chapter 1: Fractions and So Forth
		Holy Whole Numbers, Fractious Fractions
		The Distributive Property
		FOILED Again (In Praise of Distribution, Part 1)
		Factoring Polynomials (In Praise of Distribution, Part 2)
		Why Minus Times Minus is Plus (In Praise of Distribution, Part 3)
		Fractions: Two Intuitive Rules That Lead to All the Others
		Multiplying and Reducing Fractions
		Cancelling Above and Below the Bar
		The Old Multiply By 1 Trick
		(A Parenthetical Aside (On Parentheses))
		Adding and Subtracting Fractions
		Last Words and One Nasty Example
	Chapter 2: Exponents and Radicals
		Whole Number Exponents
		Negative (and Zero) Exponents
		Radical Review
		Fractional Exponents
	Chapter 3: Solving Equations
		Equivalent Equations
		How to Write and How Not to Write
		Solving Linear and Quadratic Equations
		How to Write, Part 2 (Story Problems)
		Story Problems - More Examples
		Solving Equations Containing Rational Expressions
		Solving Equations Containing Radical Expressions
		Deriving the Quadratic Formula
		Why Negative Numbers?
Part II: Geometry & Functions
	Chapter 4: Basics of Coordinate Geometry
		Coordinate Geometry: The Basic Idea
		Straight Lines: Preliminaries
		Straight Lines: The Point-Slope Form
		Straight Lines: The Slope-Intercept Form
		Pythagorean Gold Rush
		The Distance Formula
		Circles
		Six Basic Graphs
		Intersections
		Intersections (encore)
	Chapter 5: Functions
		Functions
		Function Notation
		Applied Examples
		Functions Described by Formulas
		Playing With the Difference Quotient
		Expressing A as a Function of B
		Functions Defined by Graphs...
		...and Graphs Defined by Functions
		A Preview of Your First Day of Calculus
		Functions in Science
	Chapter 6: Transformations in Coordinate Geometry
		Transformations
		Reflections
		Stretches
		Shifts
		The Transformation Table
		Preliminaries to the Proof
		The Explanation at Last
		Right-hand Side Shortcuts for *Functions*
		Graphs of Quadratic Functions
		Parabolas
		The Reflection Property of Parabolas
		Proof of the Parabola\'s Reflection Property
	Chapter 7: Exponential Functions and Logarithms
		Chess and Rice
		Exponential Growth
		Exponential Decay
		The Natural Logarithm Defined
		The Natural Logarithm\'s Inverse Properties
		The Natural Logarithm\'s Exponent Property
		Solving Exponential Equations with Logarithms
		The Natural Logarithm\'s Multiplication and Division Properties
		The Graph of the Natural Logarithm Function
		\"Unnatural\" Logarithms: Base-10 (and Others)
		Doubling Times
		The \"Rule of 70\"
		Half Lives
		Logarithms: a Tool for Solving Exponential Equations
Part III: Trigonometry
	Chapter 8: Triangle Basics
		Why Trigonometry?
		Special Pairs (and Trios) of Angles
		Which Data Determine a Triangle?
		Congruent Triangles
		Simillar Triangles
		The Pythagorean Theorem - and related shortcuts
	Chapter 9: Right-Triangle Trigonometry
		Right Makes Might: Solving Right Triangles
		Measuring Inaccessible Distances
		Interlude: Three *Exact* Values of Sine
		SOH CAH TOA: The God of Right Triangles
		Identity Crisis - and Why Cosine is Called Cosine
		The Reciprocal Trig Functions
		Basic Right-Angle Trig: Shortcuts
		Eratosthenes Measures the Earth
		How High the Moon
	Chapter 10: The Unit Circle Definitions
		Circling the Triangle: Generalizing Sine and Cosine
		But Why Generalize?
		Exact Values of Sine and Cosine at Special Angles
		Circling the Triangle II: Generalizing the Tangent Function
		Circling the Triangle III: Last Generalizations
		The Pythagorean Identity, Even and Odd Functions
	Chapter 11: Oblique Triangles
		Oblique Triangles
		The Law of Sines
		The Law of Cosines
		The Area of a Triangle: 2 Formulas
		The Area of a Triangle: Heron\'s Formula
	Chapter 12: Radians and Graphs
		Radians
		The Graphs of the Trigonometric Functions
		Transformed Sine Waves
		Graphing Transformed Trig Functions
		Calculators are Big Fakers
	Chapter 13: Identities, Inverses, Equations
		Sum Identities
		Double-Angle Identities
		Enisoc (Inverse Cosine)
		Inverse Sine and Tangent
		Solving Trigonometric Equations
Selected Answers to Exercises
	Ch. 1 Answers
	Ch. 2 Answers
	Ch. 3 Answers
	Ch. 4 Answers
	Ch. 5 Answers
	Ch. 6 Answers
	Ch. 7 Answers
	Ch. 8 Answers
	Ch. 9 Answers
	Ch. 10 Answers
	Ch. 11 Answers
	Ch. 12 Answers
	Ch. 13 Answers
Index