Cbr (3).docx

CRITICAL BOOK REPORT

IDENTITY OF TRIGONOMETRY

CREATED BY: GROUP V NADYA ANANDA BR SEMBIRING (4181111027) ELKANA INDAH SARI PAKPAHAN ( 4183312004) THASYA LEONITA PANE (4183111108) Dosen Pembimbing : Andrea Arifsyah Nasution, S.Pd., M.Sc. (198606042015041002)

Bilingual Mathematics Education 2018 MATHEMATICS DEPARTEMENT FACULTY OF MATHEMATICS AND SCIENCES STATE UNIVERSITY OF MEDAN2018

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PREFACE Praise and gratitude for the presence of the Almighty God, because of his mercy and grace, we are from group V can complete this critical book report (CBR) on time. The title of this CBR is "Identity of Trigonometry". This CBR is structured to fulfill one of the general Trigonometry course assignments. On this occasion we would like to Andrea Arifsyah Nasution, S.Pd., M.Sc.as a lecturer in trigonometry courses who have supported us in the completion of this CBR . We also want to thank the parties who helped in making this CBR which we cannot mention one by one. This CBR preparation is far from perfect, and this is a good step from the real study. Therefore we are very hopeful of constructive criticism and suggestions from the readers. Hopefully this CBR can be useful for compilers in particular and for general readers. Medan, February 22nd 2019

Group V

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CONTENTS PREFACE ...................................................................................................................................................... i CONTENTS.................................................................................................................................................. ii CHAPTER I .................................................................................................................................................. 1 INTRODUCTION ........................................................................................................................................ 1 1.1

Background ................................................................................................................................. 1

1.2

Purpose of CBR ........................................................................................................................... 1

1.3

Benefit of CBR............................................................................................................................. 1

1.4

Book’s Identity ............................................................................................................................ 1

CHAPTER II................................................................................................................................................. 3 BOOK SUMMARY...................................................................................................................................... 3 CHAPTER III ............................................................................................................................................... 3 DISCUSSION ............................................................................................................................................... 3 CHAPTER IV ............................................................................................................................................... 3 CONCLUSION ............................................................................................................................................. 3 BIBLIOGRAPHY ........................................................................................................................................ iii ATTACHMENT .......................................................................................................................................... iv

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CHAPTER I INTRODUCTION 1.1 Background This critical book review is the one of 6 assignment in KKNI curriculum and the assignmentof course name Trigonometry. Make this critical book review to make easier for readers to choose reference about identity of trigonometry and to get information explained from one book to another book. 1.2 Purpose of CBR - To review two books. - To fulfill the assignment in course Trigonometry. - And get information about Identity of Trigonometry from one book to another book. 1.3 Benefit of CBR - To add knowledge about identity of trigonometry from one book to another book. - To find the difference between one book to another book. 1.4 Book’s Identity Book 1 1. Title 2. Edition 3. Author 4. Publisher 5. City of publication 6. Year of publication 7. ISBN

: Trigonometry for Dummies : The Second Edition : Mary Jane Sterling : John Wiley & Sons, Inc : Canada : 2014 : 978-1-118-82746-8

Book 2 1. Title 2. Edition 3. Author 4. Publisher 5. City of publication 6. Year of publication 7. ISBN

: Geometry and Trygonometry : The Second Edition : Patrick D. Barry : WP(Woodhead Publishing) : USA : 2015 : 978-0-12-805066-8

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CHAPTER II BOOK SUMMARY BOOK I Identities are divided into different types, or categories, in order to help you remember them more easily and figure out when to use them more efficiently. Flipping Functions on Their Backs: Reciprocal Identities Here’s how the reciprocal identities are defined:  The reciprocal of sine is cosecant : 1 sin csc θ = θ  The reciprocal of cosine is secant : 1 cos sec θ = θ  The reciprocal of tangent is cotangent: 1 tan cot θ = θ  The reciprocal of cotangent is tangent: 1 cot tan θ = θ  The reciprocal of secant is cosine : 1 sec cos θ = θ  The reciprocal of cosecant is sine : 1 csc sin θ = θ In true fashion, when you multiply the reciprocals together, you get 1: sin θ · csc θ = 1 cos θ · sec θ = 1 tan θ · cot θ = 1 Function to Function: Ratio Identities Trig has two identities called ratio identities. The ratio identities create ways to write tangent and cotangent by using the other two basic functions, sine and cosine. The ratio identities are tan 𝜃 =

sin 𝜃 cos 𝜃

and tan 𝜃 =

cos 𝜃 sin 𝜃

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Opposites Attract: Opposite-Angle Identities The opposite-angle identities change expressions with negative angles to equivalences with positive angles. Negative angles are great for describing a situation, but they aren’t really handy when it comes to sticking them in a trig function and calculating that value. The opposite-angle identities for the three most basic functions are sin(–θ) = –sin θ cos(–θ) = cos θ tan(–θ) = –tan θ Revisiting the Classic Theorem: Pythagorean Identities The Pythagorean identities are building blocks for many of the manipulations of equations and expressions. They provide a generous number of methods for solving problems more efficiently, because they allow you to write complicated expressions in a much simpler form.

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The Pythagorean identities are sin2 θ + cos2 θ = 1 tan2 θ + 1 = sec2 θ 1 + cot2 θ = csc2 θ The exponential notation used in these identities is peculiar to trigonometry. The expression sin2 θ actually means (sin θ)2 Combining the Identities  Sine in terms of cosine  Sine in terms of tangent

: 𝑠𝑖𝑛𝜃 = ± √1 − 𝑐𝑜𝑠 2 𝜃 : sin 𝜃 =

 Sine in terms of cotangent : sin 𝜃 =  Sine in terms of secant

: 𝑠𝑖𝑛𝜃 =

 Sine in terms of cosecant : 𝑠𝑖𝑛𝜃 =

tan 𝜃 ±√𝑡𝑎𝑛2 𝜃+1 1 ±√1+𝑐𝑜𝑡 2 𝜃 ±√𝑠𝑒𝑐 2 − 1 𝑠𝑒𝑐𝜃 1 𝑐𝑠𝑐𝜃

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BOOK II Cosine and Sine of An Angle 𝑐𝑜𝑠 𝛼 =

|𝐴,𝑃|−|𝑄,𝑈| |𝐴,𝑃|

𝑠𝑖𝑛 𝛼 =

|𝐴, 𝑃| − |𝑅, 𝑉| |𝐴, 𝑃|

AB = x = 𝑐𝑜𝑠 𝛼 AR = y = 𝑠𝑖𝑛 𝛼

Subtraction of Angles cos(−𝛼) = cos 𝛼 sin(−𝛼) = − sin 𝛼

Addition of Angles cos(𝛼 ± 𝛽) = cos 𝛼 cos 𝛽 ∓ sin 𝛼 cos 𝛽 sin(𝛼 ± 𝛽) = sin 𝛼 cos 𝛽 ∓ cos 𝛼 sin 𝛽 Integer Multiples of An Angle cos(2𝛼) = 𝑐𝑜𝑠 2 𝛼 − 𝑠𝑖𝑛2 𝛼 = 2𝑐𝑜𝑠 2 𝛼 − 1 = 1 − 2𝑠𝑖𝑛2 𝛼 𝑠𝑖𝑛(2𝛼) = 2 cos 𝛼 sin 𝛼 Standard multiples of a right-angle Cos(α +900) = −sinα , sin(α +900 ) = cosα, Cos(α +1800 ) = −cosα , sin(α +1800 ) = −sinα, Cos(α +2700 ) = sinα , sin(α +2700 ) = −cosα.

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CHAPTER III DISCUSSION 1. both of these books have the same vocabulary which is trigonometric identity in addition to providing formulas, these two books are also equipped with embodiments from the existing formula. The format of writing in these two books is neat and orderly, but in book 1 the format presented is more interesting than the second book besides that the language and symbols used are familiar, but in the second book uses symbols that are slightly different for ordinary people if they are a little confused they did not read the book from the beginning

2. the difference in material between the 2 books is fast in book 1 -cosine and sine of angle -addition of angles -integrer multipler of an angles -standard multiples of right angle in book 2 -reciprocat identities -ratio identities -phytagorean identities -combining the identities

3. both of these books do not provide examples of questions that can make students understand better

4. reviewed from the exercise presented the second book contains 5 questions that can make the reader think creatively in using the existing formula to answer the questions, but the first book does not present practice

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CHAPTER IV CONCLUSION In conclusion, from criticizing these two books, we can find out that a better book is the first book in terms of writing and language and symbols in learning, but rather the second book in terms of interesting training exercises, and we know that this book has various parts. different learning Both of these books are very good and good in learning mathematics for the laity, and many

new

things

can

be

seen

from

this

book

with

different

titles.

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BIBLIOGRAPHY Mary Jane Sterling. 2014. Trigonometry for Dummies. Canada: John Wiley & Sons, Inc.

iii

ATTACHMENT BOOK I

iv

BOOK II

v