4. In
mathematics, the sine and cosine
function is a trigonometric function of an
angle.
5.
The sine function is commonly used to model
periodic phenomena such as sound and light
waves, the position and velocity of harmonic
oscillators, sunlight intensity and day length, and
average temperature variations throughout the
year.
The sine and cosine can be traced to the jyā and
koṭi-jyā functions used in Gupta period Indian
astronomy (Aryabhatiya, Surya Siddhanta), via
translation from Sanskrit to Arabic and then from
Arabic to Latin.
6. Jyā and koti-jyā
Jyā, koti-jyā are trigonometric functions introduced
by Indian astronomers and mathematicians.
These are functions of arcs of circles and not
functions of angles.
Jyā and koti-jyā are closely related to the modern
trigonometric functions of sine and cosine.
In fact, the origins of the modern terms of "sine" and
"cosine" has been traced back to the Sanskrit
words jyā and koti-jyā.
7. MODERN TERMS FOR JYĀ AND KOTI-JYĀ
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" .
8. FROM JYĀ TO SINE
The origins of the modern term sine have been
traced to the Sanskrit word jyā.
It has already been noted that the Sanskrit word
jīvā had been used as a synonym for jyā.
Sine The name sine came to us from the Latin
sinus, a term related to a curve, fold, or hollow.
The use in mathematics probably comes about
through the incorrect translation of a Sanskrit word.
9. Arab mathematicians in the eighth century
transliterated the Sanskrit word jya into the
proximate sound of jiba
Later changed it into jaib (with the same
consonants as jiba), which is a good Arabic word,
meaning a bay or a cove.
This word that was later translated by Gherardo of
Cremona (circa 1150) into its equivalent Latin word
for a bay or a cove, viz., sinus, from which the
modern term “sine” is derived."
