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.