Aryabhata, an Indian mathematician from the 5th century, made several important contributions to trigonometry. He used the term "ardha-jya" which later came to be known as "sine". Aryabhata also worked on approximating the value of pi and may have realized it was irrational. He established a place-value system with zero as a placeholder, which was a crucial concept for developing mathematics. Aryabhata also defined trigonometric ratios like sine, cosine, and tangent that are still used today.

1. ARYABHATTA
AND
TRIGONOMETRY

2. WHAT IS TRIGONOMETRY ? ? ?
• Trigonometry in basic words is the mathematics of
triangles and trigonometric functions.
• The word “Trigonometry” comes from the Greek
words: ‘Trigonon’ meaning ‘triangle’ and ‘metron’
meaning a ‘measure’.
• In a broader sense, trigonometry is that branch if
mathematics which deals with the measurement of the
sides and the angles of a triangle and the problems
allied with angles.

4. ORIGIN OF ‘SINE’
• The first use of the idea of
‘sine’ in the way we use it
today was in the work
Aryabhatiyam by Aryabhata
in A.D. 500.
• Aryabhata used the word
‘ardha-jya’ for the half chord
which came to be known as
‘jiva’ in due course.
• Later, ‘jiva’ came to be
known as ‘sinus’ and later as
‘sine’.
• An English Professor
Edmund Gunter (1581-1626)
first used the abbreviated
notation ‘sin’ .

5. Edmund Gunter
(1581 –1626)
cosinus

6. COSINE AND TANGENT
• The origin of the terms ‘cosine’ and ‘tangent’ was much later. The
cosine function arose from the need to compute the sine of the
complementary angle.
• Aryabhata called ‘kotijya’.
• The name cosinus originated with Edmund Gunter. In 1674, the
English Mathematician Sir Jonas Moore first used the abbreviated
notation ‘cos’

7. THE
TRIGONOMETRIC
RATIOS The Cosecant, Secant, and Cotangent
are the Reciprocals of
the Sine, Cosine , and Tangent respectively
Function Abbr. Description
Sine sin Opposite
Hypotenuse
Cosine cos Adjacent
Hypotenuse
Tangent tan Opposite
Adjacent
Cotangent cot Adjacent
Opposite
Secant sec Hypotenuse
Adjacent
Cosecant cosec Hypotenuse
Opposite

8. SOME MORE
WORKS OF
ARYABHATTA
• Place value system and zero
The place-value system, first seen in the 3rd century Bakhshali
Manuscript, was clearly in place in his work. While he did not use
a symbol for zero, the French mathematician Georges
Ifrah explains that knowledge of zero was implicit in
Aryabhata's place-value system as a place holder for the powers
of ten with null coefficients.

9. WORKS OF ARYABHATTA
– Approximation of π
Aryabhata worked on the approximation for pi (π), and may
have come to the conclusion that π is irrational. In the
second part of theAryabhatiyam (gaṇitapāda 10), he writes:
caturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.
"Add four to 100, multiply by eight, and then add 62,000. By this
rule the circumference of a circle with a diameter of 20,000
can be approached.“
This implies that the ratio of the circumference to the diameter
is ((4 + 100) × 8 + 62000)/20000 = 62832/20000 = 3.1416,
which is accurate to five significant figures.
π