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Exploring the wonders of Trigonometry



By Samar Bhatia

Is trigonometry tricky? Well, for many it is, for many it isn’t. So, let’s explore the uniqueness of this branch of mathematics concerned with relationships between angles and ratios of lengths.

I. The Foundations of Trigonometry: Trigonometry, a captivating branch of mathematics, delves into the study of ratios and angles within right-angled triangles. Familiar formulas include:

●      Sine (sin): P/H or opposite/hypotenuse

●      Cosine (cos): B/H or adjacent/hypotenuse

●      Tangent (tan): P/B or opposite/adjacent

Beyond these common formulas, there are additional ones such as:

  • Cosecant (csc) A: 1/Sin or Hypotenuse/Opposite
  • Secant (sec) A: 1/Csc A = Hypotenuse/Adjacent

●      Cotangent (cot) A: 1/Tan = Adjacent/Opposite

II. Tracing the historical roots: The history of trigonometry dates back to ancient civilizations. Sumerian astronomers, followed by Babylonians, employed a division of circles into 360 degrees for angle measurement. They explored ratios in related triangles. Hellenistic mathematicians like Euclid and Archimedes in the third century BC formulated theorems equivalent to modern trigonometric formulas, focusing on properties of chords and inscribed angles in circles.

It was in 140 BC that Hipparchus, from Nicaea, Asia Minor, introduced chord tables, resembling contemporary sine value tables. Ptolemy, a Greco-Egyptian astronomer, meticulously crafted trigonometric tables, known as Ptolemy’s table of chords, in the second century AD, as documented in Book 1, chapter 11 of his Almagest.