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The straight line joining the two extremities of an arc of a circle is like the string of a bow and this line is a chord of the circle. This chord is called a ''jyā'' which in [[Sanskrit]] means "a bow-string".

The straight line joining the two extremities of an arc of a circle is like the string of a bow and this line is a chord of the circle. This chord is called a ''jyā'' which in [[Sanskrit]] means "a bow-string".

The word ''jīvá'' is also used as a synonym for ''jyā'' in geometrical literature.

The word ''jīvá'' is also used as a synonym for ''jyā'' in geometrical literature.

At some point,  Indian astronomers and mathematicians realised that computations would be  more convenient if one used the halves of the chords instead of the full chords and associated the half-chords with the halves of the arcs.<ref name="Datta" /> The half-chords were called ''ardha-jyā''s or ''jyā-ardha''s. These terms were again shortened to ''jyā'' by omitting the qualifier ''ardha'' which meant "half of".

At some point,  Indian astronomers and mathematicians realised that computations would be  more convenient if one used the halves of the chords instead of the full chords and associated the half-chords with the halves of the arcs. The half-chords were called ''ardha-jyā''s or ''jyā-ardha''s. These terms were again shortened to ''jyā'' by omitting the qualifier ''ardha'' which meant "half of".

The Sanskrit word ''koṭi'' has the meaning of "point, cusp", and specifically "the [[Recurve bow|curved end of a bow]]".

The Sanskrit word ''koṭi'' has the meaning of "point, cusp", and specifically "the [[Recurve bow|curved end of a bow]]".

In trigonometry, it came to denote "the complement of an arc to 90°". Thus  

In trigonometry, it came to denote "the complement of an arc to 90°". Thus  

''koṭi-jyā'' is  "the ''jyā'' of the complementary arc". In Indian treatises, especially in commentaries, ''koṭi-jyā'' is often abbreviated as ''kojyā''. The term ''koṭi'' also denotes "the side of a right angled triangle". Thus ''koṭi-jyā'' is the base/Run of a right triangle with ''jyā'' being the perpendicular/rise .<ref name="Datta" />

''koṭi-jyā'' is  "the ''jyā'' of the complementary arc". In Indian treatises, especially in commentaries, ''koṭi-jyā'' is often abbreviated as ''kojyā''. The term ''koṭi'' also denotes "the side of a right angled triangle". Thus ''koṭi-jyā'' is the base/Run of a right triangle with ''jyā'' being the perpendicular/rise .

''Utkrama'' means "inverted", thus  ''utkrama-jyā'' means "inverted chord". The tabular values of ''utkrama-jyā'' are derived from the tabular values of ''jyā''  by subtracting the elements from the radius in the reversed order. This is really the arrow between the bow and the bow-string and hence it has also  been called ''bāṇa'', ''iṣu'' or ''śara'' all meaning "arrow".<ref name="Datta" />

''Utkrama'' means "inverted", thus  ''utkrama-jyā'' means "inverted chord". The tabular values of ''utkrama-jyā'' are derived from the tabular values of ''jyā''  by subtracting the elements from the radius in the reversed order. This is really the arrow between the bow and the bow-string and hence it has also  been called ''bāṇa'', ''iṣu'' or ''śara'' all meaning "arrow".

An arc of a circle which subtends an angle of 90° at the center is called a ''vritta-pāda'' (a quadrat of a circle). Each zodiacal sign defines an arc of 30° and three consecutive zodiacal signs defines a ''vritta-pāda''. The ''jyā'' of a ''vritta-pāda'' is the radius of the circle. The Indian astronomers coined the term ''tri-jyā'' to denote the radius of the base circle, the term ''tri-jyā'' being indicative of "the ''jyā'' of three signs". The radius is also called ''vyāsārdha'', ''viṣkambhārdha'', ''vistarārdha'', etc., all meaning "semi-diameter".<ref name="Datta" />

An arc of a circle which subtends an angle of 90° at the center is called a ''vritta-pāda'' (a quadrat of a circle). Each zodiacal sign defines an arc of 30° and three consecutive zodiacal signs defines a ''vritta-pāda''. The ''jyā'' of a ''vritta-pāda'' is the radius of the circle. The Indian astronomers coined the term ''tri-jyā'' to denote the radius of the base circle, the term ''tri-jyā'' being indicative of "the ''jyā'' of three signs". The radius is also called ''vyāsārdha'', ''viṣkambhārdha'', ''vistarārdha'', etc., all meaning "semi-diameter".

   

   

According to one convention,  the functions ''jyā'' and ''koti-jyā'' are respectively denoted by "Rsin" and "Rcos" treated as single words.<ref name="Datta" /> Others denote ''jyā'' and ''koti-jyā'' respectively by "Sin" and "Cos" (the first letters being capital letters in contradistinction to the first letters being small letters in ordinary sine and cosine functions).<ref name="Glen" />

According to one convention,  the functions ''jyā'' and ''koti-jyā'' are respectively denoted by "Rsin" and "Rcos" treated as single words. Others denote ''jyā'' and ''koti-jyā'' respectively by "Sin" and "Cos" (the first letters being capital letters in contradistinction to the first letters being small letters in ordinary sine and cosine functions).

===From jyā to sine===

===From jyā to sine===

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