Trig

The origins of right triangle geometry

3000 BCE

The Egyptians used special right triangles to survey land by measuring out 3-4-5 right triangles to make right angles.

Egyptains creat portable sundial called shadow stick used to measure time of day

1500 BCE

Thales invents Right and similar Triangles

624 BCE

Pythagoras discovers the Pythagorean theorem

570 BCE

"The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides." Though we name this theorem after the Greek mathematician Pythagoras who lived approximately 570−495 BC, it was known and recorded by the Babylonian mathematicians about 1000 years earlier. It was also discovered independently by other ancient civilisations in Mesopotamia, India and China.

Hipparchus invents trigonometry

125 BCE

debated over whether he invented it or not

Ptolemy produces a table of chords

2

The table of chords, created by the Greek astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's Almagest, a treatise on mathematical astronomy. It is essentially equivalent to a table of values of the sine function. Ptolemy expanded on Hipparchus's work and created a table of his own on chord values. He also developed the sum and difference formulas of sine and cosine

India contributes to Trig

5

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.

Law of Sines is Discovered

990

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

Sum and Difference Identities are discovered

1150

Bhaskara II, an Indian mathmetician of the 12th century, was the first to develope the formulas:
sin(a+b)=sin(a)+(cos)(a)sin(b)
sin(a-b)=sin(a)cos(b)-cos(a)sin(b)

Translation of ptolmey's furthers developement

1175

Gerardo of cremona works to translate the works of ptolmey and Hipparchus from Arab into Latin

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

1400

The indian mathematician, Madhava, 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

1596

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

Euler published his formula

1748

Eulers famous identity is published:
e^(ix) = cos(x) + isin(x)