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  • 1
    Online-Ressource
    Online-Ressource
    Boston, MA :Birkhäuser Boston :
    UID:
    almahu_9947362871002882
    Umfang: X, 229 p. , online resource.
    ISBN: 9781461201496
    Inhalt: 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.
    Anmerkung: 0 Trigonometry -- 1 Trigonometric Ratios in a Triangle -- 2 Relations among Trigonometric Ratios -- 3 Relationships in a Triangle -- 4 Angles and Rotations -- 5 Radian Measure -- 6 The Addition Formulas -- 7 Trigonometric Identities -- 8 Graphs of Trigonometric Functions -- 9 Inverse Functions and Trigonometric Equations.
    In: Springer eBooks
    Weitere Ausg.: Printed edition: ISBN 9780817639143
    Sprache: Englisch
    Schlagwort(e): Aufgabensammlung
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Online-Ressource
    Online-Ressource
    Boston, MA : Birkhäuser
    UID:
    gbv_1655006258
    Umfang: Online-Ressource (X, 229p. 185 illus, online resource)
    ISBN: 9781461201496
    Serie: SpringerLink
    Inhalt: Trigonometry, a work in the collection of the Gelfand School Program, is the result of a collaboration between two experienced pre-college teachers, one of whom, I.M. Gelfand, is considered to be among our most distinguished living mathematicians. His impact on generations of young people, some now mathematicians of renown, continues to be remarkable. Trigonometry covers all the basics of the subject through beautiful illustrations and examples. The definitions of the trigonometric functions are geometrically motivated. Geometric relationships are rewritten in trigonometric form and extended. The text then makes a transition to the study of algebraic and analytic properties of trigonometric functions, in a way that provides a solid foundation for more advanced mathematical discussions. Throughout, the treatment stimulates the reader to think of mathematics as a unified subject. Like other I.M. Gelfand treasures in the program-Algebra, Functions and Graphs, and The Method of Coordinates-Trigonometry is written in an engaging style, and approaches the material in a unique fashion that will motivate students and teachers alike. From a review of Algebra, I.M. Gelfand and A. Shen, ISBN 0-8176-3677-3: "The idea behind teaching is to expect students to learn why things are true, rather than have them memorize ways of solving a few problems, as most of our books have done. [This] same philosophy lies behind the current text by Gel'fand and Shen. There are specific 'practical' problems but there is much more development of the ideas.. [The authors] have shown how to write a serious yet lively book on algebra." -R. Askey, The American Mathematics Monthly
    Weitere Ausg.: ISBN 9780817639143
    Weitere Ausg.: Erscheint auch als Druck-Ausgabe Gelʹfand, Izrailʹ M., 1913 - 2009 Trigonometry Boston : Birkhäuser, 2001 ISBN 9780817639143
    Weitere Ausg.: ISBN 0817639144
    Weitere Ausg.: ISBN 3764339144
    Sprache: Englisch
    Fachgebiete: Mathematik
    RVK:
    Schlagwort(e): Trigonometrie
    URL: Volltext  (lizenzpflichtig)
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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