Pre–Calculus For Dummies

Grasp the principles and concepts you need to score high in pre–calculus Getting ready for calculus but feel confused? Have no fear! This un–intimidating guide walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations. You′ll understand the concepts — not just the number crunching — and see how to perform all the tasks you need to score high at exam time. Pre–calculus 101 — get a review of the Algebra II you need to know, real numbers, and how to graph, solve, and perform operations with functions What′s your angle? — take a tour of the essentials of trigonometry, from angles, right triangles, and trig ratios to graphing the parent graph of the six basic trig functions Keep it simple — discover how to simplify trig expressions and solve for an unknown variable using formulas and identities (and solve triangles that aren′t right triangles using Law of Sines and Law of Cosines) Not just plane thinking — delve into analytic geometry and system solving with the understanding of complex numbers, polar–coordinate graphing, conics, systems of equations, sequences, and more Open the book and find: An overview of pre–calculus Tips on graphing trig functions like a pro How to apply the major theorems and formulas The lowdown on analytic geometry Guidance on identifying limits and continuity The 4–1–1 on working with a graphing calculator The laws for solving oblique triangles Everything you need to prepare for calculus Learn to: Grasp essential pre–calculus topics Apply the major theorems and formulas Tackle proofs with confidence and ease

Introduction 1 Part I: Set It Up, Solve It, Graph It 7 Chapter 1: Pre–Pre–Calculus 9 Chapter 2: Playing with Real Numbers 21 Chapter 3: The Building Blocks of Pre–Calc: Functions 33 Chapter 4: Digging Out and Using Roots to Graph Polynomial Functions 67 Chapter 5: Exponential and Logarithmic Functions 97 Part II: The Essentials of Trigonometry 117 Chapter 6: Circling in on Angles 119 Chapter 7: Simplifying the Graphing and Transformation of Trig Functions 149 Chapter 8: Identifying with Trig Identities: The Basics 181 Chapter 9: Advanced Identities: Your Keys to Pre–Calc Success 201 Chapter 10: Taking Charge of Oblique Triangles with the Laws of Sines and Cosines 223 Part III: Analytic Geometry and System Solving 243 Chapter 11: Plane Thinking: Complex Numbers and Polar Coordinates 245 Chapter 12: Slicing Cones or Measuring the Path of a Comet — with Confidence 261 Chapter 13: Streamlining Systems, Managing Variables 291 Chapter 14: Sequences, Series, and Expanding Binomials for the Real World 325 Chapter 15: Scouting the Road Ahead to Calculus 349 Part IV: The Part of Tens 363 Chapter 16: Ten Habits to Develop as You Prepare for Calculus 365 Chapter 17: Ten Habits to Quit Before Calculus 373 Index 379

Yang Kuang , PhD, is a professor of mathematics at Arizona State University. He currently serves on the calculus committee where he and other members discuss what and how to teach calculus to students majoring in math and physical sciences. Elleyne Kase is a professional writer.