Who Needs Trigonometry?


The word "trigonometry" originates from the Greek word "τριγωνομετρία" which is in turn is derived from the concatenation of two terms "τρίγωνο" (triangle) and "μετρεῖν" (to measure).   The Latin form is "trigonometria" which in similar fashion literally means "triangle measuring". [1]

Trigonometry is an ancient science invented of necessity by the two oldest civilizations in the world, to wit, the Babylonian along the Tigress-Euphrates river valley and the Egyptian along the Nile river valley.  More than ten millennia ago, the transition from hunter-gather societies to permanent settlements around agricultural sites ran into serious problems of soil exhaustion after a significant expenditure of time and effort in removing rocks and leveling and plowing fields.   Annual river valley floods brought restoring nutrients to such fields but obliterated markers identifying different plots.  Trigonometry restored individual and collective boundary markers.

One of the earliest Egyptian records is the “Rhind Papyrus” from the 2nd millennium BC (e.g. 1660 BC).  In about 300 B.C. Euclid’s elements was published in Alexandra providing the geometric basis for trigonometry.  The first logical and systematic study of trigonometry was compiled in the 2nd century BC by the Greek mathematician Hipparchus.  Further advances came from India and later in the middle ages from Arabia from whence it was adopted as a separate subject in the Latin West beginning in the Renaissance with Regiomontanus.   The final development of modern trigonometry came entirely from Western Europe beginning with the 17th century mathematics of Isaac Newton and James Sterling and achieved its current form with Leonhard Euler (1748).



Trigonometry has different levels of relevance are described in the following FIVE categories arranged by degrees of need in decreasing order.


Civil Engineers and surveyors use trigonometry every day to survey property lines, to determine the routes of new highways, to build dams and other structures, and for uncountable other projects.  Indeed it was for these purposes trigonometry was invented five thousand years ago.

Architects require trigonometry to design buildings, bridges, and monuments.

Aerospace engineers need trigonometry to design airplanes and model the follow of air over their wings.

Spherical trigonometry is essential for navigation and astronomy as well as for plotting the trajectories of rockets and spacecraft.


Anyone whose job requires mathematical expertise at any level.  Trigonometry is essential to understanding calculus, differential equations, and almost all forms of advanced mathematics.

Physicists use trigonometry in all of their endeavors.

Electrical engineers use trigonometry for signal processing, for circuit design and antennae design, and for most other sub-specialties as well.

Mechanical engineers use trigonometry to design mechanical linkages and in many other ways.


Chemists and Chemical Engineers occasionally require trigonometry in the study of chemical reaction rates.

Biologists occasionally require trigonometry as in the study of predator-prey relationships.


Social Scientists who occasionally encounter an equation need the mathematics surrounding trigonometry.

Convicts planning an escape by digging a tunnel need trigonometry.


The marginalized in our society who have jobs requiring no education even less need mathematics of any sort.  Some of these unfortunates include

High school drop-outs with careers flipping burgers in fast food restaurants.  Note this is not true for those who design fast food equipment.

The homeless with careers in panhandling and inmates of insane asylums with no careers. J



1.      History of Trigonometry, Wikipedia.