Art of problem solving, precalculus

Art of Problem Solving's Precalculus book. This book 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. Precalculus is part of the acclaimed Art of Problem Solving curriculum designed to challenge high-performing middle and high school students. Precalculus covers trigonometry, complex numbers, vectors, and matrices. It includes nearly 1000 problems, ranging from routine exercises to extremely challenging problems drawn from major mathematics competitions such as the American Invitational Mathematics Exam and the USA Mathematical Olympiad. Almost half of the problems have full, detailed solutions in the text, and the rest have full solutions in the accompanying Solutions Manual. As with all of the books in Art of Problem Solving's Introduction and Intermediate series, Precalculus is structured to inspire the reader to explore and develop new ideas. Each section starts with problems, so the student has a chance to solve them without help before proceeding. The text then includes solutions to these problems, through which new techniques are taught. Important facts and powerful problem solving approaches are highlighted throughout the text. Functions review Introduction to trigonometric functions Trigonometric identities Applications to geometry Parameterization and trigonometric coordinate systems Basics of complex numbers Trigonometry and complex numbers Geometry of complex numbers Vectors in two dimensions Matrices in two dimensions Vectors and matrices in three dimensions, part 1 Vectors and matrices in three dimensions, part 2 Vector geometry References Hints to selected problems. 1.Functions Review 2.Intro to trig functions 3.Trig identities 4.Applications to Geometry 5.Parameterization and Trig Coordinate Systems 6.Basics of Complex Numbers 7.Trig and Complex Numbers 8.Geometry of Complex Numbers 9.Vectors in Two Dimensions 10.Matrices in Two Dimensions 11.Vectors and Matrices in Three Dimensions, Part 1 12.Vectors and Matrices in Three Dimensions, Part 2 13.Vector Geometry