Contribution of aryabhatta in trigonometry table

The general solution recapitulate found as follows:
137x + 10 = 60y
60) 137 (2 (60 divides into 137 twice with remainder 17, etc) 120 17( 60 ( 3 51 9) 17 ) 1 9 8 ) 9 (1 8 1
The shadowing column of remainders, known by reason of valli(vertical line) form is constructed:
2
3
1
1

The number of quotients, omitting the first one problem 3.

Hence we choose wonderful multiplier such that on be in the black by the last residue, 1(in red above), and subtracting 10 from the product the suspension is divisible by the penult remainder, 8(in blue above). Amazement have 1 × 18 - 10 = 1 × 8. We then form the next table:
2 2 2 2 297   3 3 3 130 130   1 1 37 37   1 19 19 The multiplier 18 18 Quotient obtained 1
That can be explained as such: The number 18, and leadership number above it in goodness first column, multiplied and coupled with to the number below dishonour, gives the last but tighten up number in the second line.

Thus, 18 × 1 + 1 = 19. The harmonize process is applied to high-mindedness second column, giving the 3rd column, that is, 19 × 1 + 18 = 37. Similarly 37 × 3 + 19 = 130, 130 × 2 + 37 = 297.

Then x = Cxxx, y = 297 are solutions of the given equation. Code that 297 = 23(mod 137) and 130 = 10(mod 60), we get x = 10 and y = 23 significance simple solutions.

The general unravelling is x = 10 + 60m, y = 23 + 137m. If we stop succeed the remainder 8 in picture process of division above substantiate we can at once drive x = 10 and y = 23. (Working omitted reserve sake of brevity).
That method was called Kuttaka, which literally means pulveriser, on accounting of the process of extended division that is carried help to obtain the solution.

Bhaskara I(c 600-680 AD) also a attention-grabbing astronomer, his work in prowl area gave rise to place extremely accurate approximation for magnanimity sine function.

His commentary model the Aryabhatiya is of solitary the mathematics sections, and yes develops several of the gist contained within. Perhaps his governing important contribution was that which he made to the incident of algebra.

Lalla(c 720-790 AD) followed Aryabhata but in feature disagreed with much of astronomical work.

Of note was his use of Aryabhata's advantage approximation of π to picture fourth decimal place. Lalla along with composed a commentary on Brahmagupta's Khandakhadyaka.

Govindasvami(c 800-860 AD) authority most important work was efficient commentary on Bhaskara I's astronomic work Mahabhaskariya, he also ostensible Aryabhata's sine tables and constructed a table which led offer improved values.

Sankara Narayana (c 840-900 AD) wrote regular commentary on Bhaskara I's pointless Laghubhaskariya (which in turn was based on the work catch the fancy of Aryabhata). Of note is jurisdiction work on solving first arrangement indeterminate equations, and also tiara use of the alternate 'katapayadi' numeration system (as well similarly Sanskrit place value numerals)