ENGLISH

Exact Values in Trigonometry: Five New Techniques

By Bhava Nath Dahal

Book information

Publisher
CreateSpace Independent Publishing Platform
Year
2016
ISBN
1536995002, 9781536995008
Language
english
Format
PDF
Filesize
1 MB (1131129 bytes)
Edition
1
Pages
106\150
Library
Mobilism
Time added
2021-10-22 09:38:37

Description

Since last 2500 years, respectful mathematicians worked for trigonometric values differently. The determined 6-major and further 10 less-common trigonometric ratios. Many modern mathematicians worked for EXACT values too. In this book, there are five methods for determination of trigonometric ratios. One, named as Vatsa-method is ratio-based. It discovered new sum of natural number theory of 'vatsa'. Remaining four methods are based on chord (a) and supplementary chords (b) or their product (ab). We can find EXACT trigonometric values for all integer angles and polygons; for the remaining concept of 'appropriate accuracy' adopted herewith. For example, square root of 3 is irrational. Therefore, so-called exact value of Sine based on square root 3 is not exact, rather with 'appropriate accuracy' for the user. Same concept has used for 'appropriate accuracy'. In this book, trigonometric ratios are determined under: 1. Arc-Line method (1/2 to 1 hour to study or teaching) 2. Series method (1 hour to study or teaching) 3. Angle-Rewritten method (1 hour to study or teaching) 4. Precise-Rewritten method (1/2 to 1 hour to study or teaching) 5. Vatsa method (1 hour to study or teaching) This book developed new method for trigonometric values with basis of 'square root of 2' only. Chapter 1 TRIGONOMETRIC RATIO 1.1 Trigonometric Ratios 1.2 Historical development 1.3 Geometric Method 1.4 Chord and Supplementary Chord 1.4.1 Half angle Chords 1.4.2 Double angle Chords 1.4.3 Triple angle Chords 1.4.4 Addition and subtraction of Chords 1.4.5 Calculated Chords 1.5 Sine Square 1.6 Sine Scale Chapter 2 ARC-LINE METHOD 2.1 Arc-Line concept 2.1.1 Inputs 2.1.2 Accuracy 2.1.3 Mathematical process 2.2 Trigonometric Ratios of any angle 2.3 Angle-based Formula Chapter 3 SERIES-METHOD 3.1 Exact Sine from Series Method 3.1.1 Angle and Complementary-angle Series 3.1.2 Sine of A/2n-Series Chapter 4 ANGLE-REWRITTEN METHOD 4.1 Exact Sine of an Angle 4.1.1 Half-Series 4.1.2 Varieties of Techniques for Angle-Rewritten 4.2 General procedures - exact value Chapter 5 PRECISE-REWRITTEN METHOD 5.1 Precise-Rewritten Concept 5.1.1 Inputs 5.1.2 Accuracy 5.1.3 Mathematical process 5.2 Sine of any angle Chapter 6 VATSA METHOD 6.1 Ratio-based Sine Table 6.1.1 For Sexagesimal System (Degrees) 6.1.2 For Metric System (Grades) 6.2 Accuracy 6.3 Sine of an Individual Angle Chapter 7 Vasta- Natural Number Series 7.1 New Method for Series-Sum 7.1.1 First Series (Sum of Arithmetic Series) 7.1.2 Nth Series 7.2 Sum of Series of Sequence

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