Exact Values in Trigonometry

the long version

Since last 2500 years, respectful mathematicians worked for trigonometric values differently. Now, 6-major trigonometric ratios are in use. Less-common but there are further 10 trigonometric ratios. Many modern mathematicians worked for exact values too. They developed much, still left room for many angles. 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'. Four methods are based on chord (a) and supplementary chords (b) or their product (ab). We can find exact radicals for numerous angles; 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) In fact, the maximum study or teaching time for five method is one working day for the person having general trigonometric knowledge.