History
Where Did the Word Trigonometry Come from?
According to the Encyclopaedia Britannica, "The word trigonometry comes from the Greek words trigonon (“triangle”) and metron (“to measure”)". By putting these two concepts together, we can see that trigonometry defined is the study of the measurements of the angles and side lengths of a triangle. Specifically we study the ratio that exists between two side lengths of a right triangle while taking into account or being able to find the measurement of an angle of the triangle.
How and Why were Trig Functions Developed?
According to Heathh in his "A History of Brief Mathetics" he states, "the prime application of trigonometry in past cultures, not just ancient Greek, is to astronomy. Computation of angles in the celestial sphere requires a different kind of geometry and trigonometry than that in the plane. The geometry of the sphere was called "spherics" and formed one part of the quadrivium of study. Various authors, including Euclid, wrote books on spherics. The current name for the subject is "elliptic geometry." Trigonometry apparently arose to solve problems posed in spherics rather than problems posed in plane geometry. Thus, spherical trigonometry is as old as plane trigonometry".
Babylonians
Sometime before 300 B.C.E., the Babylonians had developed a meaurements system for angles. Their numeral system was based upon the number 60 and they managed to figure out a way to classify angles in degrees. Additionally, the Babylonians utilized trigonometry for astronomy. They were the first people to mark stars by coordinates and measure longitude and latitude in degrees.
Hipparchus
Eventually, the Babylonian practice of measuring angles in degrees spread to Greece. The Greeks start making use of chords and noticing ratios and patterns associated with them. About 150 B.C.E., the astronomer Hipparchus began his work on trigonometry, after making many several great astrological advancements. His work with the chord led him to write a 12-book detailing his findings and create the first trigonometric table. Even though his book has since been lost, Hipparchus is credited as the Father of Trigonometry. His work led mathematicians to begin considering using the 360 degree method we have today to describe circles.
Ptolomy
Greek astronomer Ptolomy took Hipparchus's ideas and began to work them out. He is most well known for putting forth the idea for the geocentric model of the universe which, although untrue, led to the eventual development of the heliocentric model of the universe. Due to Hipparchus's influence, Ptolomy was able to publish his own book of chords which also hinted a strong Babylonian influence, mostly due to the division of the circle into 360 degrees. It is believed that his work utilized something similar to what is now the Pythagorean identity, even though trigonometric functions did not exist at this point.
Trigonometry!
It wasn't until about the 12th century that the work of Hipparchus and Ptolomy was translated into Latin, sparking trigonometric study in a new group of people. These ideas move from Latin to Greek in the 16th century, when the name trigonometry was developed. This led to the development of the specific trigonometric functions by French mathematician, Albert Girard. He started using the abbreviations sin, cos, and tan to describe the ratios between sides of a triangle.
To view a presentation by Savannah Martinez of the timeline of the development of trigonometry, click here.