Trigonometric Functions (Problem Solving Approach)
| Date: 21 April 2011, 03:49
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From the Authors:
By tradition, trigonometry is an important component
of mathematics courses at high school, and trigonometry
questions are always set at oral and written examinations
to those entering universities, engineering colleges,
and teacher-training institutes.
The aim of this study aid is to help the student to master
the basic techniques of solving difficult problems in
trigonometry using appropriate definitions and theorems
from the school course of mathematics. To present the
material in a smooth way, we have enriched the text
with some theoretical material from the textbook Algebra
and Fundamentals of Analysis edited by Academician
A. N. Kolmogorov and an experimental textbook of the
same title by Professors N.Ya. Vilenkin, A.G. Mordkovich,
and V.K. Smyshlyaev, focussing our attention on
the application of theory to solution of problems. That
is why our book contains many worked competition
problems and also some problems to be solved independently
(they are given at the end of each chapter, the
answers being at the end of the book).
Some of the general material is taken from Elementary
Mathematics by Professors G.V. Dorofeev, M.K. Potapov,
and N.Kh. Rozov (Mir Publishers, Moscow, 1982), which
is one of the best study aids on mathematics for precollege
students.
We should like to note here that geometrical problems
which can be solved trigonometrically and problems
involving integrals with trigonometric functions are
not considered.
At present, there are several problem hooks on mathematics
(trigonometry included) for those preparing to
pass their entrance examinations (for instance, Problems
at Entrance Examinations in Mathematics by Yu.V. Nesterenko,
S.N. Olekhnik, and M.K. Potapov (Moscow,
Nauka, 1983); A Collection of Competition Problems in
Mathematics with Hints and Solutions edited by A.I. PriIepko
(Moscow, Nauka, 1986); A Collection of Problems in
Mathematics for Pre-college Students edited by A. I. Prilepko
(Moscow, Vysshaya Shkola, 1983); A Collection of
Competition Problems in Mathematics for Those Entering
Engineering Institutes edited by M.1. Skanavi (Moscow,
Vysshaya Shkola, 1980). Some problems have been borrowed
from these for our study aid and we are grateful
to their authors for the permission to use them.
The beginning of a solution to a worked example is
marked by the symbol .... and its end by the symbol ~.
The symbol ~ indicates the end of the proof of a statement.
Our book is intended for high-school and pre-college
students. We also hope that it will be helpful for the
school children studying at the "smaller" mechanicomathematical
faculty of Moscow State University.
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