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Art of Problem Solving's Precalculus goes above and beyond the average high school precalculus class, yet it requires little background knowledge. This is good for high school math competition preparation. Overall, this book is extremely conceptual.
How to Use This Book
Acknowledgements
Functions Review
Function Basics.
Graphing Functions
Composition
Inverse Functions
Summary
Introduction to Trigonometric Functions
The Unit Circle
Radians
Graphs of Trigonometric Functions
Transformations of Trigonometric Functions
Inverse Trigonometric Functions
Summary
Trigonometric Identities
Introduction to Trigonometric Identities
Sums and Differences of Angles
Double and Half Angles
Sum-to-product and Product-to-sum .
Problem Solving with Identities
Summary
Applications to Geometry
Right Triangle Trigonometry
Law of Cosines
Law of Sines
More Triangle Relationships
Summary
Parameterization and Trigonometric Coordinate Systems
Param eterization
Polar Coordinates
Coordinates in Three Dimensions
Summary
Basics of Complex Numbers
Complex Number Arithmetic
The Complex Plane
Real and Imaginary Parts
Nonreal Roots of Polynomials
Summary
Trigonometry and Complex Numbers
Polar Form of Complex Numbers
Exponential Form of Complex Numbers
Roots of Unity
Problems Involving Roots of Unity
Summary
Geometry of Complex Numbers
Transformations of the Complex Plane
Parallel and Perpendicular Lines
Distance
Regular Polygons
Classic Theorems
Summary
Vectors in Two Dimensions
What's a Vector?
The Dot Product
Lines and Linear Dependence
Projections
Summary
Matrices in Two Dimensions
What is a Matrix?
Multiplying Matrices
Matrices as Transformations
The Determinant
Geometric Interpretation of the Determinant
Inverting a Matrix
Summary
Vectors and Matrices in Three Dimensions, Part 1
Vectors in Three Dimensions
3 x 3 Matrices
Determinants of 3 x 3 Matrices
More Than Just 2 x 2 and 3 x 3
Summary
Vectors and Matrices in Three Dimensions, Part 2
Lines and Planes in Three Dimensions
More Planes in Three Dimensions.
The Cross Product
Geometric Interpretation of the Determinant
Inverse of a 3 x 3 M atrix
Summary
Vector Geometry
Introduction
Vectors in the Triangle
Vectors, Complex Numbers, and Challenging Problems
Summary
References 488
Hints to Selected Problems
Index