Madhava's sine table

Madhava's sine table is the table of trigonometric sines constructed by the 14th century Kerala mathematician-astronomer Madhava of Sangamagrama (c. 1340 – c. 1425). The table lists the jya-s or Rsines of the twenty-four angles from 3.75° to 90° in steps of 3.75° (1/24 of a right angle, 90°). Rsine is just the sine multiplied by a selected radius and given as an integer. In this table, as in Aryabhata's earlier table, R is taken as 21600 ÷ 2π ≈ 3437.75.

The table is encoded in the letters of the Sanskrit alphabet using the Katapayadi system, giving entries the appearance of the verses of a poem.

Madhava's original work containing the table has not been found. The table is reproduced in the Aryabhatiyabhashya of Nilakantha Somayaji (1444–1544) and also in the Yuktidipika/Laghuvivrti commentary of Tantrasamgraha by Sankara Variar (circa. 1500–1560).^{: 114–123}

The verses below are given as in Cultural foundations of mathematics by C.K. Raju.^{: 114–123} They are also given in the Malayalam Commentary of Karanapaddhati by P.K. Koru but slightly differently.