Jagannatha had Jai Singh Sawai as his patron. Jai Singh Sawai was the ruler of Amber, now Jaipur, in eastern Rajasthan. He began his rule in 1699 and by clever use of tax rights on land that was rented by the state to an individual person he became the most important ruler in the region. His financial success let him finance the scholarly works of people such as Jagannatha. It is worth noting that Jai Singh's importance was recognised by Amber which was then called Jaipur in his honour.
Jai Singh ruled Amber throughout the period in which Jagannatha was producing his scientific work. He realised that the health of the country required Indian culture and science to be revitalised and returned to its position of leading importance which it had possessed. So Jai Singh employed Jagannatha to make Sanskrit translations of the important Greek scientific works which at that time were only available in Arabic translations.
Jagannatha translated Euclid's Elements from the Arabic translation by Nasir al-Din al-Tusi made nearly 500 years earlier. His Sanskrit version was called Rekhaganita and it was completed by 1727. We know this date since a copy was made by a scribe and he dated the start of his work as 1727.
Ptolemy's Almagest Ⓣ had been one of the works which Arabic scientists had studied intently and, in 1247, al-Tusi wrote Tahrir al-Majisti (Commentary on the Almagest) in which he introduced various trigonometrical techniques to calculate tables of sines. Jagannatha translated al-Tusi's Arabic version but he did more than this for he included in the same work, which he called Siddhantasamrat, his own comments on related work of other Arabic mathematical astronomers such as Ulugh Beg and al-Kashi.
It is clear from Jagannatha's work that he is working as one of a group of mathematicians and astronomers gathered by Jai Singh in his scheme to bring the best in scientific ideas from outside India to reinvigorate the scientific scene in India.
In  Gupta looks at the history of the result
sin(π/10) = (√5 - 1)/4
in Indian mathematics. The result appears for the first time in the work of Bhaskara II, but there were a number of interesting proofs of the result by later Indian mathematicians. One of the proofs presented by Gupta in  was by Jagannatha who gave a proof which was essentially geometric in nature but, interestingly, contained an analytic procedure in terms of trigonometric and algebraic steps.
Article by: J J O'Connor and E F Robertson