# Trigonometry with the Ancient Indian Mathematicians

The most significant development of trigonometry in ancient times was in India. Influential works from the $$4^{th}$$ & the $$5^{th}$$ century AD, known as Siddhantas first defined the sine as the relationship between half an angle & half a chord, while also defining the cosine, versine ($$1-$$ cosine) & inverse sine.

Soon afterwards, another Indian mathematician & astronomer Aryabhata collected & expanded upon the developments of the Siddhantas in a path breaking work, the Aryabhatiya. The Siddhantas & the Aryabhatiya contain the earliest survivng tables of sine & versine values, in $$3.75^\circ$$ intervals from $$0^\circ$$ to $$90^\circ$$, to an accuracy of $$4$$ decimal places. They used the words jya for sine, kojya for cosine, utkrama-jya for versine & otkram jya for inverse sine. The words jya & kojya eventually became sine & cosine after a mistranslation.

Aryabhata was the first one. Others after him expanded on these works of trigonometry. In the $$6^{th}$$ century AD, Varahamihira discovered the identity $$sin^2x + cos^2x = 1$$. He improved Aryabhata's sine table & discovered an early version of the Pascal's Triangle.

Such was the ingenuity of the ancient Indian mathematicians!

Note by Ameya Salankar
4 years ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

Great Indians great mathematics

- 2 years, 2 months ago