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BIRKHAUSER BOSTON INC BIRKHAUSER BOSTON INC Trigonometry by I.M. Gelfand Mark Saul
In a sense trigonometry sits at the center of high school mathematics. It originates in the study of geometry when we investigate the ratios of sides in similar right triangles or when we look at the relationship between a chord of a circle and its arc. It leads to a much deeper study of periodic functions and of the socalled transcendental functions which cannot be described using finite algebraic processes. It also has many applications to physics astronomy and other branches of science. It is a very old subject. Many of the geometric results that we now state in trigonometric terms were given a purely geometric exposition by Euclid. Ptolemy an early astronomer began to go beyond Euclid using the geometry of the time to construct what we now call tables of values of trigonometric functions. Trigonometry is an important introduction to calculus where one stud ies what mathematicians call analytic properties of functions. One of the goals of this book is to prepare you for a course in calculus by directing your attention away from particular values of a function to a study of the function as an object in itself. This way of thinking is useful not just in calculus but in many mathematical situations. So trigonometry is a part of precalculus and is related to other precalculus topics such as exponential and logarithmic functions and complex numbers.show more