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Trigonometry (Hardcover, 2001 ed.)
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Trigonometry (Hardcover, 2001 ed.)
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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 so-called 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 pre-calculus, and is related to other
pre-calculus topics, such as exponential and logarithmic functions,
and complex numbers."
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