Pauls Online Math NotesThe field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. Throughout history, trigonometry has been applied in areas such as geodesy , surveying , celestial mechanics , and navigation. Trigonometry is known for its many identities ,   which are equations used for rewriting trigonometrical expressions to solve equations, to find a more useful expression, or to discover new relationships. Sumerian astronomers studied angle measure, using a division of circles into degrees. The ancient Nubians used a similar method. In the 3rd century BC, Hellenistic mathematicians such as Euclid and Archimedes studied the properties of chords and inscribed angles in circles, and they proved theorems that are equivalent to modern trigonometric formulae, although they presented them geometrically rather than algebraically.
Algebra And Trigonometry
Introduction to Algebra and Trigonometry provides a complete and self-contained presentation of the fundamentals of algebra and trigonometry. This book describes an axiomatic development of the foundations of algebra, defining complex numbers that are used to find the roots of any quadratic equation. Advanced concepts involving complex numbers are also elaborated, including the roots of polynomials, functions and function notation, and computations with logarithms. This text also discusses trigonometry from a functional standpoint. The angles, triangles, and applications involving triangles are likewise treated.
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Algebra and Trigonometry presents the essentials of algebra and trigonometry with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered. Comprised of 11 chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of algebraic notation and practical manipulative skills such as factoring, using exponents and radicals, and simplifying rational expressions is highlighted, along with the most common mistakes in algebra. The reader is then introduced to the solution of linear, quadratic, and other types of equations and systems of equations, as well as the solution of inequalities.
Welcome to my online math tutorials and notes. In other words, they do not assume you've got any prior knowledge other than the standard set of prerequisite material needed for that class. The assumptions about your background that I've made are given with each description below. I'd like to thank Fred J. I've tried to proof read these pages and catch as many typos as I could, however it just isn't possible to catch all of them when you are also the person who wrote the material.