Geometry with Trigonometry

Geometry with Trigonometry

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Geometry with Trigonometry Second Edition is a second course in plane Euclidean geometry, second in the sense that many of its basic concepts will have been dealt with at school, less precisely. It gets underway with a large section of pure geometry in Chapters 2 to 5 inclusive, in which many familiar results are efficiently proved, although the logical frame work is not traditional. In Chapter 6 there is a convenient introduction of coordinate geometry in which the only use of angles is to handle the perpendicularity or parallelism of lines. Cartesian equations and parametric equations of a line are developed and there are several applications. In Chapter 7 basic properties of circles are developed, the mid-line of an angle-support, and sensed distances. In the short Chaper 8 there is a treatment of translations, axial symmetries and more generally isometries. In Chapter 9 trigonometry is dealt with in an original way which e.g. allows concepts such as clockwise and anticlockwise to be handled in a way which is not purely visual. By the stage of Chapter 9 we have a context in which calculus can be developed. In Chapter 10 the use of complex numbers as coordinates is introduced and the great conveniences this notation allows are systematically exploited. Many and varied topics are dealt with , including sensed angles, sensed area of a triangle, angles between lines as opposed to angles between co-initial half-lines (duo-angles). In Chapter 11 various convenient methods of proving geometrical results are established, position vectors, areal coordinates, an original concept mobile coordinates. In Chapter 12 trigonometric functions in the context of calculus are treated.

New to this edition:

The second edition has been comprehensively revised over three years
Errors have been corrected and some proofs marginally improved
The substantial difference is that Chapter 11 has been significantly extended, particularly the role of mobile coordinates, and a more thorough account of the material is given
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Product details

  • Hardback | 280 pages
  • 152 x 229 x 19.05mm | 420g
  • Academic Press Inc
  • San Diego, United States
  • English
  • 2nd edition
  • black & white illustrations
  • 0128050667
  • 9780128050668
  • 1,396,347

Table of contents

1 - Preliminaries

2 - Basic shapes of geometry

3 - Distance; degree-measure of an angle

4 - Congruence of triangles; parallel lines

5 - The parallel axiom; Euclidean geometry

6 - Cartesian coordinates; applications

7 - Circles; their basic properties

8 - Translations; axial symmetries; isometries

9 - Trigonometry; cosine and sine; addition formulae

10 - Complex coordinates; sensed angles; angles between lines

11 - Vector and complex-number methods

12 - Trigonometric functions in calculus

Appendix A - List of Axioms

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Review quote

"The book is carefully written, and proceeds at a fairly high level of sophistication... Instructors who want to present a completely rigorous development of the subject and who are therefore willing to accept the pedagogical risks involved, will certainly want to look at this text." --MAA Reviews, Geometry with Trigonometry, Second Edition
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About Patrick Barry

Patrick D. Barry, National University of Ireland, Ireland
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