History of Trigonometry

By CJ_Hanson
  • Period: 125 to 180

    First Trigonometric Tables

    The first table compiled on trigonometric values of arc and chord for a series of angle measurements was created by Hipparchus of Nicaea
  • Claudius Ptolemy's Theorems
    147

    Claudius Ptolemy's Theorems

    AD
    Ptolemy expanded on Hipparchus's work and created a table of his own on chord values. He also develeoped the first evidence of several trigonometric identities in his Almagest, such as the half-angle formula, and the sum and difference formulas of sine and cosine.
  • 150

    First Trigonometric Tables

    BCE.
    The first table compiled on trigonometric values of arc and chord for a series of angle measurements was created by Hipparchus of Nicaea
  • Further Developments of Sine and Cosine Tables
    499

    Further Developments of Sine and Cosine Tables

    Aryabhata, an Indian mathematician and astronomer, expanded on the works of the Siddhantas and created many sine and cosine tables. He published these works in the Aryabhatiya.
  • 500

    Trionometry Moves to India

    AD
    Major developments are made in India in the fifth and sixth centuries by the five Siddhantas (Indian philosophies), which outlined the conventions of trigonometric ratios and how they are used in astronomical observations.
  • Jan 1, 820

    First Table of Tangents

    AD
    Muhammad ibn Mūsā al-Khwārizmī develops the first table of tangents of certain measures of angles.
  • Jan 1, 830

    First Table of Cotangents

    AD
    Habash al-Hasib al-Marwazi developes the first table of cotangent values of certain angle measurements.
  • Jan 1, 875

    First Tables of Cosecant and Secant

    AD
    Muhammad ibn Jābir al-Harrānī al-Battānī developes the first tables of the reciprocal functions secant and cosecant for certain angle measures.
  • Jan 1, 990

    Law of Sines is Discovered

    AD
    Abū al-Wafā' al-Būzjānī, a Persian mathematician is using all six trigonometric functions, and developes the Law of Sines for spherical trigonometry.
  • Jan 1, 1150

    Sum and Difference Identites are Discovered

    AD
    Bhaskara II, an Indian mathematician of the 12th century, was the first to develope the formulas
    sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
    sin(a-b)=sin(a)cos(b)-cos(a)sin(b)
  • Jan 1, 1400

    Madhava Uses Inifinte Taylor Series to Expand Sine, Cosine, Tangent and Arctangent

    AD
    The indian mathematician uses what will become to be known as Taylor series expansions to produce the values of trigonometric functions with a new record of accuracy. He also developed expansion series for pi.

  • Right Triangle Trigonometry is Invented

    After trigonometry finally makes its way to Western Europe, Georg Joachim Rheticus, a student of Copernicus, is the first to define all six trigonometric functions in terms of right triangles in his work, The Opus palatinum de triangulis.

  • Euler's Formula

    Euler's famous identity is published.
    e ^ (ix) = cos (x) + isin (x)