Jya ( Sine ), Kotijya ( Cosine ) and Utkram Jya ( Versine ) are the three trignometric functions introduced by the Indian astronomers and mathematicians.
In order to compute the celestial longitudes of planets, these functions were used by the trinity of Indian Astronomy, Bhaskara, Brahnmagupta and Aryabhata.
Thrijya, the Radius or R
If 360 = 2 Pi r
then, r = 360/2Pi in degrees
One degree is 60 minutes and one minute is 60 seconds and hence one degree is 3600 seconds.
R in seconds will be ((360/2pi)* 3600 ) Vikalas or 206265 seconds. This figure 206265 is known as the Magic Figure of Astronomy.
Bhujajya = R Sin
Kotijya = R Cos
The arc sine of the angle is Bhujachapa
The arc cosine of the angle is Kotichapa
The arc tangent of the angle is Sparshachapa
By Jya, Bramhmagupta meant 5 degrees of a sign of 30 degrees. Hence a Zodiacal Sign consists of 6 Jyas ( 30 degrees ) . The Zodiac of 360 degrees was divided into 4 quarters of 90 degrees each. Three Jyas of 30 degrees each becomes a quadrant of the Zodiac and was called Thrijya. Thrijya is also the Radius, the Vyasardha.
His magnum opus, the Brahmasphuta Siddhanta was translated by the Arabs as As Sind Hind. Jya became jiba and Kotijya became kojiba in Arabic. It was translated into Latin as sinus ( meaning ” bosom ” ). So Sinus and Co-sinus when translated into English became Sine and Cosine !
The Aryabhateeyam of Aryabhata was translated by the Arabs as Al Arjabhat. Trignometry is derived from the Sanskrit Thrikonamithi and Geometry from Jyamithi !