Learning Trigonometry By Problem Solving
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Learning Trigonometry By Problem Solving
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Author : Alexander Rozenblyum
language : en
Publisher: World Scientific
Release Date : 2021-06-25
Learning Trigonometry By Problem Solving written by Alexander Rozenblyum and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-25 with Mathematics categories.
In this book, trigonometry is presented mainly through the solution of specific problems. The problems are meant to help the reader consolidate their knowledge of the subject. In addition, they serve to motivate and provide context for the concepts, definitions, and results as they are presented. In this way, it enables a more active mastery of the subject, directly linking the results of the theory with their applications. Some historical notes are also embedded in selected chapters.The problems in the book are selected from a variety of disciplines, such as physics, medicine, architecture, and so on. They include solving triangles, trigonometric equations, and their applications. Taken together, the problems cover the entirety of material contained in a standard trigonometry course which is studied in high school and college.We have also added some interesting, in our opinion, entertainment problems. To solve them, no special knowledge is required. While they are not directly related to the subject of the book, they reflect its spirit and contribute to a more lighthearted reading of the material.
103 Trigonometry Problems
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Author : Titu Andreescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-06
103 Trigonometry Problems written by Titu Andreescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-06 with Mathematics categories.
* Problem-solving tactics and practical test-taking techniques provide in-depth enrichment and preparation for various math competitions * Comprehensive introduction to trigonometric functions, their relations and functional properties, and their applications in the Euclidean plane and solid geometry * A cogent problem-solving resource for advanced high school students, undergraduates, and mathematics teachers engaged in competition training
115 Trigonometry Problems From The Awesomemath Summer Program
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Author : Titu Andreescu
language : en
Publisher:
Release Date : 2017-11
115 Trigonometry Problems From The Awesomemath Summer Program written by Titu Andreescu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11 with Trigonometry categories.
Focusing on Trigonometry reveals a wealth of alternate approaches to solving intricate geometry problems while providing foundational support in other areas of mathematics such as Fourier Analysis and Differential Equations. It is time for Trigonometry to receive the attention it deserves in this stand-alone book where the theory chapter is an invaluable pedagogical resource with lots of examples and guided exercises and the subsequent chapters offer a collection of carefully selected introductory through advanced problems and solutions intended to enhance the problem-solving skills of the reader. This book is not only for those studying for mathematics Olympiads but all individuals who want a better understanding of Trigonometry so they will be more successful in different settings such as a calculus course. This book offers a comprehensive overview of the trigonometric functions and contains a collection of 115 carefully selected introductory and advanced problems in Trigonometry from world-wide renowned Olympiads and mathematical magazines, as well as original problems designed by the authors. Together with the beautiful examples and the creative solutions, the present text is a valuable resource and teaching material for anybody who wants to explore the beauty of Trigonometry.
Trigonometry
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Author : James Tanton
language : en
Publisher: The Mathematical Association of America
Release Date : 2015-08-10
Trigonometry written by James Tanton and has been published by The Mathematical Association of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-10 with Mathematics categories.
This guide covers the story of trigonometry. It is a swift overview, but it is complete in the context of the content discussed in beginning and advanced high-school courses. The purpose of these notes is to supplement and put into perspective the material of any course on the subject you may have taken or are currently taking. (These notes will be tough going for those encountering trigonometry for the very first time!)
Algebra And Trigonometry Problem Solver
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Author : Jerry R. Shipman
language : en
Publisher: Research & Education Assoc.
Release Date : 2012-05
Algebra And Trigonometry Problem Solver written by Jerry R. Shipman and has been published by Research & Education Assoc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05 with Mathematics categories.
Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies. Here in this highly useful reference is the finest overview of algebra and trigonometry currently available, with hundreds of algebra and trigonometry problems that cover everything from algebraic laws and absolute values to quadratic equations and analytic geometry. Each problem is clearly solved with step-by-step detailed solutions. DETAILS - The PROBLEM SOLVERS are unique - the ultimate in study guides. - They are ideal for helping students cope with the toughest subjects. - They greatly simplify study and learning tasks. - They enable students to come to grips with difficult problems by showing them the way, step-by-step, toward solving problems. As a result, they save hours of frustration and time spent on groping for answers and understanding. - They cover material ranging from the elementary to the advanced in each subject. - They work exceptionally well with any text in its field. - PROBLEM SOLVERS are available in 41 subjects. - Each PROBLEM SOLVER is prepared by supremely knowledgeable experts. - Most are over 1000 pages. - PROBLEM SOLVERS are not meant to be read cover to cover. They offer whatever may be needed at a given time. An excellent index helps to locate specific problems rapidly. - Educators consider the PROBLEM SOLVERS the most effective and valuable study aids; students describe them as "fantastic" - the best books on the market. TABLE OF CONTENTS Introduction Chapter 1: Fundamental Algebraic Laws and Operations Chapter 2: Least Common Multiple / Greatest Common Divisor Chapter 3: Sets and Subsets Chapter 4: Absolute Values Chapter 5: Operations with Fractions Chapter 6: Base, Exponent, Power Chapter 7: Roots and Radicals Simplification and Evaluation of Roots Rationalizing the Denominator Operations with Radicals Chapter 8: Algebraic Addition, Subtraction, Multiplication, Division Chapter 9: Functions and Relations Chapter 10: Solving Linear Equations Unknown in Numerator Unknown in Numerator and/or Denominator Unknown Under Radical Sign Chapter 11: Properties of Straight Lines Slopes, Intercepts, and Points of Given Lines Finding Equations of Lines Graphing Techniques Chapter 12: Linear Inequalities Solving Inequalities and Graphing Inequalities with Two Variables Inequalities Combined with Absolute Values Chapter 13: Systems of Linear Equations and Inequalities Solving Equations in Two Variables and Graphing Solving Equations in Three Variables Solving Systems of Inequalities and Graphing Chapter 14: Determinants and Matrices Determinants of the Second Order Determinants and Matrices of Third and Higher Order Applications Chapter 15: Factoring Expressions and Functions Nonfractional Fractional Chapter 16: Solving Quadratic Equations by Factoring Equations without Radicals Equations with Radicals Solving by Completing the Square Chapter 17: Solutions by Quadratic Formula Coefficients with Integers, Fractions, Radicals, and Variables Imaginary Roots Interrelationships of Roots: Sums; Products Determining the Character of Roots Chapter 18: Solving Quadratic Inequalities Chapter 19: Graphing Quadratic Equations / Conics and Inequalities Parabolas Circles, Ellipses, and Hyberbolas Inequalities Chapter 20: Systems of Quadratic Equations Quadratic/Linear Combinations Quadratic/Quadratic (Conic) Combinations Multivariable Combinations Chapter 21: Equations and Inequalities of Degree Greater than Two Degree 3 Degree 4 Chapter 22: Progressions and Sequences Arithmetic Geometric Harmonic Chapter 23: Mathematical Induction Chapter 24: Factorial Notation Chapter 25: Binomial Theorem / Expansion Chapter 26: Logarithms and Exponentials Expressions Interpolations Functions and Equations Chapter 27: Trigonometry Angles and Trigonometric Functions Trigonometric Interpolations Trigonometric Identities Solving Triangles Chapter 28: Inverse Trigonometric Functions Chapter 29: Trigonometric Equations Finding Solutions to Equations Proving Trigonometric Identities Chapter 30: Polar Coordinates Chapter 31: Vectors and Complex Numbers Vectors Rectangular and Polar/Trigonometric Forms of Complex Numbers Operations with Complex Numbers Chapter 32: Analytic Geometry Points of Line Segments Distances Between Points and in Geometrical Configurations Circles, Arcs, and Sectors Space-Related Problems Chapter 33: Permutations Chapter 34: Combinations Chapter 35: Probability Chapter 36: Series Chapter 37: Decimal / Factional Conversions / Scientific Notation Chapter 38: Areas and Perimeters Chapter 39: Angles of Elevation, Depression and Azimuth Chapter 40: Motion Chapter 41: Mixtures / Fluid Flow Chapter 42: Numbers, Digits, Coins, and Consecutive Integers Chapter 43: Age and Work Chapter 44: Ratio, Proportions, and Variations Ratios and Proportions Direct Variation Inverse Variation Joint and Combined Direct-Inverse Variation Chapter 45: Costs Chapter 46: Interest and Investments Chapter 47: Problems in Space Index WHAT THIS BOOK IS FOR Students have generally found algebra and trigonometry difficult subjects to understand and learn. Despite the publication of hundreds of textbooks in this field, each one intended to provide an improvement over previous textbooks, students of algebra and trigonometry continue to remain perplexed as a result of numerous subject areas that must be remembered and correlated when solving problems. Various interpretations of algebra and trigonometry terms also contribute to the difficulties of mastering the subject. In a study of algebra and trigonometry, REA found the following basic reasons underlying the inherent difficulties of both math subjects: No systematic rules of analysis were ever developed to follow in a step-by-step manner to solve typically encountered problems. This results from numerous different conditions and principles involved in a problem that leads to many possible different solution methods. To prescribe a set of rules for each of the possible variations would involve an enormous number of additional steps, making this task more burdensome than solving the problem directly due to the expectation of much trial and error. Current textbooks normally explain a given principle in a few pages written by a mathematics professional who has insight into the subject matter not shared by others. These explanations are often written in an abstract manner that causes confusion as to the principle's use and application. Explanations then are often not sufficiently detailed or extensive enough to make the reader aware of the wide range of applications and different aspects of the principle being studied. The numerous possible variations of principles and their applications are usually not discussed, and it is left to the reader to discover this while doing exercises. Accordingly, the average student is expected to rediscover that which has long been established and practiced, but not always published or adequately explained. The examples typically following the explanation of a topic are too few in number and too simple to enable the student to obtain a thorough grasp of the involved principles. The explanations do not provide sufficient basis to solve problems that may be assigned for homework or given on examinations. Poorly solved examples such as these can be presented in abbreviated form which leaves out much explanatory material between steps, and as a result requires the reader to figure out the missing information. This leaves the reader with an impression that the problems and even the subject are hard to learn - completely the opposite of what an example is supposed to do. Poor examples are often worded in a confusing or obscure way. They might not state the nature of the problem or they present a solution, which appears to have no direct relation to the problem. These problems usually offer an overly general discussion - never revealing how or what is to be solved. Many examples do not include accompanying diagrams or graphs, denying the reader the exposure necessary for drawing good diagrams and graphs. Such practice only strengthens understanding by simplifying and organizing algebra and trigonometry processes. Students can learn the subject only by doing the exercises themselves and reviewing them in class, obtaining experience in applying the principles with their different ramifications. In doing the exercises by themselves, students find that they are required to devote considerable more time to algebra and trigonometry than to other subjects, because they are uncertain with regard to the selection and application of the theorems and principles involved. It is also often necessary for students to discover those "tricks" not revealed in their texts (or review books) that make it possible to solve problems easily. Students must usually resort to methods of trial and error to discover these "tricks," therefore finding out that they may sometimes spend several hours to solve a single problem. When reviewing the exercises in classrooms, instructors usually request students to take turns in writing solutions on the boards and explaining them to the class. Students often find it difficult to explain in a manner that holds the interest of the class, and enables the remaining students to follow the material written on the boards. The remaining students in the class are thus too occupied with copying the material off the boards to follow the professor's explanations. This book is intended to aid students in algebra and trigonometry overcome the difficulties described by supplying detailed illustrations of the solution methods that are usually not apparent to students. Solution methods are illustrated by problems that have been selected from those most often assigned for class work and given on examinations. The problems are arranged in order of complexity to enable students to learn and understand a particular topic by reviewing the problems in sequence. The problems are illustrated with detailed, step-by-step explanations, to save the students large amounts of time that is often needed to fill in the gaps that are usually found between steps of illustrations in textbooks or review/outline books. The staff of REA considers algebra and trigonometry subjects that are best learned by allowing students to view the methods of analysis and solution techniques. This learning approach is similar to that practiced in various scientific laboratories, particularly in the medical fields. In using this book, students may review and study the illustrated problems at their own pace; students are not limited to the time such problems receive in the classroom. When students want to look up a particular type of problem and solution, they can readily locate it in the book by referring to the index that has been extensively prepared. It is also possible to locate a particular type of problem by glancing at just the material within the boxed portions. Each problem is numbered and surrounded by a heavy black border for speedy identification.
Basic Trigonometry In One Week With An Introduction To Brain Based Learning Bbl
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Author : Vineeth Remanan
language : en
Publisher: Vineeth Remanan
Release Date : 2021-10-16
Basic Trigonometry In One Week With An Introduction To Brain Based Learning Bbl written by Vineeth Remanan and has been published by Vineeth Remanan this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-16 with Mathematics categories.
Basic Trigonometry In One Week: With an introduction to brain based learning (BBL) This book is not a complete solution to all learning problems. But it is certainly a beginning in the right direction. It stands out from its competitors due to its radical approach to the principles and techniques of learning. The book starts off by presenting what it is and what it isn't. Then challenges the reader to self examine who they are. "Are you fast learner, or a slow learner. Are you good at math, or having a hard time with it" It goes on to discuss fast learning vs slow learning, also detailing the procedures involved in an effective learning process with an exposition on Brain Based Learning (BBL). Learning techniques like spaced repetition and active recalling using flash cards are discussed in great detail. It also discusses the benefits of meditation methods to achieve a focused mindset necessary for learning. The trigonometry part is divided into 7 chapters-"The Seven Days", each consisting of 3 sessions, making a total of 21 sessions. In addition to numerous examples and problems, the chapters contain explanations on some basic questions in mathematics like: Why can't we divide by zero? Why a complete rotation is 360 degrees? What is the difference between an equation and an identity? etc. Problem solving is regarded with high importance, since entire sessions are dedicated to them. The book features topics like: Angles and its units Trigonometric functions Pythagoras Theorem Trigonometric Identities Proving Identities Quadrants and sign convention Allied angles Double and triple angle formulae Tips and tricks for memorizing formulae at the end of each chapter. Final Quiz for final brush up And many more...
Mathematics In Action
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Author : Consortium for Foundation Mathematics
language : en
Publisher: Addison-Wesley Longman
Release Date : 2004-04
Mathematics In Action written by Consortium for Foundation Mathematics and has been published by Addison-Wesley Longman this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04 with Algebra categories.
This intermediate algebra text, based on standards in the AMATYC Crossroads document, motivates college math students to develop mathematical literacy and a solid foundation for future study in mathematics and other disciplines. This third book of a three-book series presents mathematical concepts and skills through relevant activities derived from real-life situations. These activities are meaningful to students because they illustrate how mathematics arises naturally from real-world situations and problems. The Mathematics in Action series is based on the assumption that students learn mathematics best by doing mathematics in a meaningful context. Therefore, the text takes a collaborative approach to learning. Students take an active role in their own learning by working in groups, thereby developing communication skills, a sense of independence, and a can-do attitude about mathematics. Technology is integrated throughout the book so that students learn to interpret real-life data numerically, symbolically, and graphically. this text to increase their knowledge of mathematics, their problem-solving skills, and their overall confidence in their ability to learn.
The Not So Scary Guide To Basic Trigonometry
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Author : Kevin D. Hunter
language : en
Publisher: Trafford Publishing
Release Date : 2011-04
The Not So Scary Guide To Basic Trigonometry written by Kevin D. Hunter and has been published by Trafford Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04 with Mathematics categories.
The Not-So-Scary Guide to Basic Trigonometry eliminates the fear, frustration, and anxiety often associated with learning trigonometry. By introducing a new, intuitive technique called a "mathematical tripod," author Kevin D. Hunter is able to do away with traditional, complicated algebraic methods, resulting in better comprehension and less stress. This slim but effective guide is written in a simple, straightforward style designed to make things easy for the average person who may not be well versed in the concepts of geometry or algebra. The numerous explanations, diagrams, and drawings will appeal to many different learning styles, and the provided practice problems walk readers step-by-step through the process of finding the correct answer. Those who do not have the time or the money for expensive college courses or seminars will benefit from the easy-to-learn methods introduced in this guide. Anyone with a scientific calculator and a basic understanding of multiplication and division can learn and apply the fundamentals of trigonometry. Trigonometry shouldn't be scary, and now it doesn't have to be with The Not-So-Scary Guide to Basic Trigonometry.
Must Know High School Trigonometry
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Author : Sandra Luna McCune
language : en
Publisher: McGraw Hill Professional
Release Date : 2019-12-27
Must Know High School Trigonometry written by Sandra Luna McCune and has been published by McGraw Hill Professional this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-27 with Mathematics categories.
The new Must Know series is like a lightning bolt to the brain Every school subject has must know ideas, or essential concepts, that lie behind it. This book will use that fact to help you learn in a unique way. Most study guides start a chapter with a set of goals, often leaving the starting point unclear. In Must Know High School Trigonometry, however, each chapter will immediately introduce you to the must know idea, or ideas, that lie behind the new trigonometry topic. As you learn these must know ideas, the book will show you how to apply that knowledge to solving trigonometry problems. Focused on the essential concepts of trigonometry, this accessible guide will help you develop a solid understanding of the subject quickly and painlessly. Clear explanations are accompanied by numerous examples and followed with more challenging aspects of trigonometry. Practical exercises close each chapter and will instill you with confidence in your growing trigonometry skills. Must Know High School Trigonometry features: • Each chapter begins with the must know ideas behind the new topic • Extensive examples illustrate these must know ideas • Students learn how to apply this new knowledge to problem solving • 250 practical review questions instill confidence • IRL (In Real Life) sidebars present real-life examples of the subject at work in culture, science, and history • Special BTW (By the Way) sidebars provide study tips, exceptions to the rule, and issues students should pay extra attention to • Bonus app includes 100 flashcards to reinforce what students have learned
A Romp Tour Of Trigonometry
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Author : Charles Rambo
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2017-10-31
A Romp Tour Of Trigonometry written by Charles Rambo and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-31 with categories.
Trigonometry is a sore spot for many students. Not only are the topics hard, but STEM majors see them come up again and again in their classes. Where is a student to go for help? Most trigonometry texts are either extremely expensive, shallow, or old and not well suited for current STEM curricula. Hence, the motivation for A Romp Tour of Trigonometry. It has all the topics students need and they are presented in a modern fashion. This text is designed for students going into Calculus and physics. The trigonometric identities needed for Calculus are emphasized. There is a thorough treatment of polar coordinates. Vectors are addressed, including treatment of the dot product. There are several applications of vectors, such as work and force problems, which will be helpful in physics. A Romp Tour of Trigonometry also provides a more robust theoretical backing of ideas than most trigonometry texts. Most notably it introduces the geometric study of triangles, including a study of triangle congruence and similarity of triangles. This provides students with a richer foundation on which to analyze trigonometry. The majority of students learn more easily when first introduced to ideas within a concrete setting as opposed to introducing ideas by providing general principles. Frequently, students don't even look at their books, because their texts approach concepts from a perspective that is too abstract for someone learning the material for the first time. For most students, a general understanding of ideas must be built slowly by means of analyses of specific cases. As a result, the emphasis of this text is teaching by means of examples. Abstract ideas are covered, but new ideas are always reiterated more concretely. Furthermore, the examples provide students with an enriched sense of the mathematics, because they provide intuition and explore more ways to formulate problems. A Romp Tour of Trigonometry is also unique because it doesn't solve problems the way most books do. Instead, it solves them the way students do: based on core ideas. Formulas are used sparingly, unlike in most math books. For example, A Romp Tour of Trigonometry only uses one formulation of the Law of Cosines. Usually, two formulations are provided, one for side lengths and another for angle measures. It makes solving the problems computationally easier, but almost all students forget all but one formulation voiding the benefit. The approach of this text requires more algebra, but it teaches students to solve problems in a more realistic way. Problem-solving is a critical component of learning mathematics. More than enough exercises are included for students to obtain a thorough understanding of the material. Furthermore, the problems cover a wide range of difficulty, which means A Romp Tour of Trigonometry will be helpful to trigonometry students at many skill levels.