25/09/2019

'What are sine and cosine used for?', asks Viana.

Uma das aplicações mais importantes da trigonometria foi na criação do Sistema Métrico Decimal, utilizado hoje na maior parte dos países – Imagem: Freepik

Reproduction of Marcelo Viana's column in Folha de S.Paulo.

The study of the relationships between the sides and angles of triangles, which we call trigonometry, dates back to antiquity and is one of the most central and useful areas of mathematics.

Unfortunately, in the classroom it is often reduced to a list of opaque definitions and formulas, without any mention of its important practical applications.

It's not surprising that most students don't have fond memories of them. And the strange names of trigonometric functions (sine, cosine, tangent, etc.) don't help.

In Spanish, "seno" also means "breast," and a colleague from Madrid once assured me that this was the origin of the name, referring to the rounded shape of the sine function graph. But the story is a bit more complicated.

The concept of the sine of an angle first appeared around the year 500, in the work of the Hindu mathematician and astronomer Aryabhata the Elder (476–550). He used the name “jya” (bowstring) which, through a mistranslation, became “jaib” (fold or bay) in Arabic and, later, “sinus” (fold, bay or… breast) in Latin. From this last term, popularized by Leonardo Fibonacci (1170–1250), the greatest mathematician of medieval Europe, the current name resulted.

One of the most impactful applications of trigonometry was in the creation of the Metric System, which is used in most countries today. Until the 18th century, hundreds of units of weight and measurement were used, varying from region to region and over time. The French, for example, measured length in "king's feet," with obvious inconveniences when the monarch changed. With industrialization and the growth of trade, standardizing units became urgent.

After failed attempts to create an international standard by consensus, revolutionary France took the lead. In 1790, the French Academy of Sciences appointed five notable scientists —Borda, Condorcet, Lagrange, Laplace, and Monge—to address the problem and present concrete proposals. In their report, they proposed, among other things, that the unit of length should become the "meter," defined as 1/40,000,000 of the length of a terrestrial meridian.

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