{"product_id":"2940014091237","title":"Trigonometry","description":"This book covers elementary trigonometry. It is suitable for a one-semester course at the\u003cbr\u003ecollege level, though it could also be used in high schools. The prerequisites are high school\u003cbr\u003ealgebra and geometry.\u003cbr\u003eThis book basically consists of my lecture notes from teaching trigonometry at Schoolcraft\u003cbr\u003eCollege over several years, expanded with some exercises. There are exercises at the end\u003cbr\u003eof each section. I have tried to include some more challenging problems, with hints when\u003cbr\u003eI felt those were needed. An average student should be able to do most of the exercises.\u003cbr\u003eAnswers and hints to many of the odd-numbered and some of the even-numbered exercises\u003cbr\u003eare provided in Appendix A.\u003cbr\u003eThis text probably has a more geometric feel to it than most current trigonometry texts.\u003cbr\u003eThat was, in fact, one of the reasons I wanted to write this book. I think that approaching the\u003cbr\u003esubject with too much of an analytic emphasis is a bit confusing to students. It makes much\u003cbr\u003eof the material appear unmotivated. This book starts with the “old-fashioned” right triangle\u003cbr\u003eapproach to the trigonometric functions, which is more intuitive for students to grasp.\u003cbr\u003eIn my experience, presenting the definitions of the trigonometric functions and then immediately\u003cbr\u003ejumping into proving identities is too much of a detour from geometry to analysis\u003cbr\u003efor most students. So this book presents material in a very different order than most books\u003cbr\u003etoday. For example, after starting with the right triangle definitions and some applications,\u003cbr\u003egeneral (oblique) triangles are presented. That seems like a more natural progression of\u003cbr\u003etopics, instead of leaving general triangles until the end as is usually the case.\u003cbr\u003eThe goal of this book is a bit different, too. Instead of taking the (doomed) approach that\u003cbr\u003estudents have to be shown that trigonometry is “relevant to their everyday lives” (which\u003cbr\u003einevitably comes off as artificial), this book has a different mindset: preparing students\u003cbr\u003eto use trigonometry as it is used in other courses. Virtually no students will ever in their\u003cbr\u003e“everyday life” figure out the height of a tree with a protractor or determine the angular\u003cbr\u003espeed of a Ferris wheel. Students are far more likely to need trigonometry in other courses\u003cbr\u003e(e.g. engineering, physics). I think that math instructors have a duty to prepare students\u003cbr\u003efor that.\u003cbr\u003eIn Chapter 5 students are asked to use the free open-source software Gnuplot to graph\u003cbr\u003esome functions. However, any program can be used for those exercises, as long as it produces\u003cbr\u003eaccurate graphs. Appendix B contains a brief tutorial on Gnuplot.\u003cbr\u003eThere are a few exercises that require the student to write his or her own computer program\u003cbr\u003eto solve some numerical computation problems. There are a few code samples in Chapter\u003cbr\u003e6, written in the Java and Python programming languages, hopefully sufficiently clear\u003cbr\u003eso that the reader can figure out what is being done even without knowing those languages.\u003cbr\u003eiii\u003cbr\u003eiv PREFACE\u003cbr\u003eOctave and Sage are also mentioned. This book probably discusses numerical issues more\u003cbr\u003ethan most texts at this level (e.g. the numerical instability of Heron’s formula for the area\u003cbr\u003eof a triangle, the secant method for solving trigonometric equations). Numerical methods\u003cbr\u003eprobably should have been emphasized even more in the text, since it is rare when even a\u003cbr\u003emoderately complicated trigonometric equation can be solved with elementary methods, and\u003cbr\u003esince mathematical software is so readily available.\u003cbr\u003eI wanted to keep this book as brief as possible. Someone once joked that trigonometry\u003cbr\u003eis two weeks of material spread out over a full semester, and I think that there is some\u003cbr\u003etruth to that. However, some decisions had to be made on what material to leave out. I had\u003cbr\u003eplanned to include sections on vectors, spherical trigonometry - a subject which has basically\u003cbr\u003evanished from trigonometry texts in the last few decades (why?) - and a few other topics,\u003cbr\u003ebut decided against it. The hardest decision was to exclude Paul Rider’s clever geometric\u003cbr\u003eproof of the Law of Tangents without using any sum-to-product identities, though I do give\u003cbr\u003ea reference to it.","brand":"WDS Publishing","offers":[{"title":"Default Title","offer_id":47083415372016,"sku":"2940014091237","price":5.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/2940014091237_p0.jpg?v=1763600464","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/2940014091237","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}