tag:open.umn.edu,2005:/opentextbooks/subjects/geometry-and-trigonometryOpen Textbook Library - Geometry and Trigonometry Textbooks2021-11-15T19:55:38Zhttps://open.umn.edu/assets/common/favicon/favicon-1594c2156c95ca22b1a0d803d547e5892bb0e351f682be842d64927ecda092e7.icohttps://open.umn.edu/assets/library/otl_logo-f9161d5c999f5852b38260727d49b4e7d7142fc707ec9596a5256a778f957ffc.png10972021-11-15T19:55:38Z2024-01-22T14:52:28ZTrigonometry<img alt="Read more about Trigonometry" title="Trigonometry cover image" class="cover " width="144" height="154" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MzA3NSwicHVyIjoiYmxvYl9pZCJ9fQ==--1310ba8fce333d0e01b0e36154ed07a9a951b850/cover.png" />This text covers the content of a standard trigonometry course, beginning with a review of facts from geometry.10712021-10-06T19:04:28Z2024-01-22T14:52:28ZEuclid's Elements Redux<img alt="Read more about Euclid's Elements Redux" title="Euclid's Elements Redux cover image" class="cover " width="675" height="788" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MjkyMSwicHVyIjoiYmxvYl9pZCJ9fQ==--73c450f44e2bd9709ca7939404d48a190ae907a5/Capture.JPG" />"Euclid's 'Elements' Redux" is an open textbook on mathematical logic and geometry based on Euclid's "Elements" for use in grades 7-12 and in undergraduate college courses on proof writing. Many problem solvers throughout history wrestled with Euclid as part of their early education including Copernicus, Kepler, Galileo, Sir Isaac Newton, Ada Lovelace, Abraham Lincoln, Bertrand Russell, and Albert Einstein. This edition is part of an effort to ensure that tomorrow's great thinkers will have that same privilege.7432019-07-13T17:04:42Z2024-01-22T14:52:05ZGeometry with an Introduction to Cosmic Topology<img alt="Read more about Geometry with an Introduction to Cosmic Topology" title="Geometry with an Introduction to Cosmic Topology cover image" class="cover " width="333" height="499" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NjkwLCJwdXIiOiJibG9iX2lkIn19--132753694cc067d8ff9bdc36fea634ae2957fcab/978-1717134813.jpg" />Motivated by questions in cosmology, the open-content text Geometry with an Introduction to Cosmic Topology uses Mobius transformations to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe. The text, written for students who have taken vector calculus, also explores the interplay between the shape of a space and the type of geometry it admits. Geometry is suitable for a semester course in non-Euclidean geometry or as a guide to independent study, with over 200 exercises and several essays on topics including the history of geometry, parallax and curvature, and research aimed at determining the shape of the universe.6112018-09-16T18:13:09Z2024-01-22T14:52:01ZTrigonometry<img alt="Read more about Trigonometry" title="Trigonometry cover image" class="cover " width="645" height="833" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NTM3LCJwdXIiOiJibG9iX2lkIn19--f63c3626153e21ac5dfaf3dbfe0caf4cc3905d48/0000Trigonome.PNG" />The precursors to what we study today as Trigonometry had their origin in ancient Mesopotamia, Greece and India. These cultures used the concepts of angles and lengths as an aid to understanding the movements of the heavenly bodies in the night sky. Ancient trigonometry typically used angles and triangles that were embedded in circles so that many of the calculations used were based on the lengths of chords within a circle. The relationships between the lengths of the chords and other lines drawn within a circle and the measure of the corresponding central angle represent the foundation of trigonometry - the relationship between angles and distances.6102018-09-16T17:45:37Z2024-01-22T14:52:01ZCollege Algebra & Trigonometry<img alt="Read more about College Algebra & Trigonometry" title="College Algebra & Trigonometry cover image" class="cover " width="648" height="834" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NTM2LCJwdXIiOiJibG9iX2lkIn19--f2a5e683dc84d820ff8096d0bd5df979135c76c1/0000CollegAlg.PNG" />This College Algebra text will cover a combination of classical algebra and analytic geometry, with an introduction to the transcendental exponential and logarithmic functions. If mathematics is the language of science, then algebra is the grammar of that language. Like grammar, algebra provides a structure to mathematical notation, in addition to its uses in problem solving and its ability to change the appearance of an expression without changing the value.5082018-09-07T17:22:06Z2024-01-22T14:51:57ZElementary College Geometry - 2021 ed.<img alt="Read more about Elementary College Geometry - 2021 ed." title="Elementary College Geometry - 2021 ed. cover image" class="cover " width="402" height="562" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6Mzk4NCwicHVyIjoiYmxvYl9pZCJ9fQ==--e77af57592fcbd3f4af559dfa1772beec1a3109c/Screen%20Shot%202022-09-05%20at%203.49.40%20PM.png" />This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra. The emphasis is on applying basic geometric principles to the numerical solution of problems. For this purpose the number of theorems and definitions is kept small. Proofs are short and intuitive, mostly in the style of those found in a typical trigonometry or precalculus text. There is little attempt to teach theorem-proving or formal methods of reasoning. However the topics are ordered so that they may be taught deductively. The problems are arranged in pairs so that just the odd-numbered or just the even-numbered can be assigned. For assistance, the student may refer to a large number of completely worked-out examples. Most problems are presented in diagram form so that the difficulty of translating words into pictures is avoided. Many problems require the solution of algebraic equations in a geometric context. These are included to reinforce the student's algebraic and numerical skills, A few of the exercises involve the application of geometry to simple practical problems. These serve primarily to convince the student that what he or she is studying is useful. Historical notes are added where appropriate to give the student a greater appreciation of the subject. This book is suitable for a course of about 45 semester hours. A shorter course may be devised by skipping proofs, avoiding the more complicated problems and omitting less crucial topics.4882018-09-07T17:22:05Z2024-01-22T14:51:57ZTrigonometry<img alt="Read more about Trigonometry" title="Trigonometry cover image" class="cover " width="1066" height="1342" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDE2LCJwdXIiOiJibG9iX2lkIn19--2d9fe4cdd382b18c504c7f114883ef0b87753106/0000Trigonome.png" />This trigonometry textbook is different than other trigonometry books in that it is free to download, and the reader is expected to do more than read the book and is expected to study the material in the book by working out examples rather than just reading about them. So this book is not just about mathematical content but is also about the process of learning and doing mathematics. That is, this book is designed not to be just casually read but rather to be engaged. Since this can be a difficult task, there are several features of the book designed to assist students in this endeavor. In particular, most sections of the book start with a beginning activity that review prior mathematical work that is necessary for the new section or introduce new concepts and definitions that will be used later in that section. Each section also contains several progress checks that are short exercises or activities designed to help readers determine if they are understanding the material. In addition, the text contains links to several interactive Geogebra applets or worksheets. These applets are usually part of a beginning activity or a progress check and are intended to be used as part of the textbook.4342018-09-07T17:22:02Z2024-01-22T14:51:56ZEuclidean plane and its relatives<img alt="Read more about Euclidean plane and its relatives" title="Euclidean plane and its relatives cover image" class="cover " width="280" height="420" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6Mjk1OSwicHVyIjoiYmxvYl9pZCJ9fQ==--1ffd5fd7eb8aa75da07f686bbc21eeb1da2eb6f6/front.png" />This book is meant to be rigorous, conservative, elementary and minimalist. At the same time it includes about the maximum what students can absorb in one semester. Approximately one-third of the material used to be covered in high school, but not any more.The present book is based on the courses given by the author at the Pennsylvania State University as an introduction to the foundations of geometry. The lectures were oriented to sophomore and senior university students. These students already had a calculus course. In particular,they are familiar with the real numbers and continuity. It makes it possible to cover the material faster and in a more rigorous way than it could be done in high school.2392018-09-07T17:21:50Z2024-01-22T14:52:31ZAlgebra and Trigonometry 2e<img alt="Read more about Algebra and Trigonometry 2e" title="Algebra and Trigonometry 2e cover image" class="cover " width="824" height="1060" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6MzcwNSwicHVyIjoiYmxvYl9pZCJ9fQ==--a7fde398cfa52fa9a6ff2a9081f4a4b290008235/Screen%20Shot%202022-05-27%20at%2011.39.02%20AM.png" />Algebra and Trigonometry 2e provides a comprehensive exploration of mathematical principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. The modular approach and the richness of content ensure that the book addresses the needs of a variety of courses. Algebra and Trigonometry 2e offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned. The Algebra and Trigonometry 2e revision focused on improving relevance and representation as well as mathematical clarity and accuracy. Introductory narratives, examples, and problems were reviewed and revised using a diversity, equity, and inclusion framework. Many contexts, scenarios, and images have been changed to become even more relevant to students’ lives and interests. To maintain our commitment to accuracy and precision, examples, exercises, and solutions were reviewed by multiple faculty experts. All improvement suggestions and errata updates from the first edition were considered and unified across the different formats of the text. The first edition of Algebra and Trigonometry by OpenStax is available in web view here.572018-09-07T17:21:40Z2024-01-22T14:51:46ZCollege Trigonometry<img alt="Read more about College Trigonometry" title="College Trigonometry cover image" class="cover " width="239" height="315" data-controller="cover" data-placeholder="/assets/common/placeholder-0e0607cbc50663ddb9e8fd188058bcd2630c730ef6ee322801278607b7d5af8e.png" src="/rails/active_storage/blobs/redirect/eyJfcmFpbHMiOnsiZGF0YSI6NDUsInB1ciI6ImJsb2JfaWQifX0=--5e07daa661a62ff1d4004152c5436f5e74162641/0000CollegeTr.png" />Covers chapters 10-11 of Precalculus.
https://open.umn.edu/opentextbooks/subjects/geometry-and-trigonometry?page=2