Applications of trigonometry
What can you do with trig? Historically, it was developed for astronomy and geography, but scientists
have been using it for centuries for other purposes, too. Besides other fields of mathematics, trig
is used in physics, engineering, and chemistry. Within mathematics, trig is used in primarily in
calculus (which is perhaps its greatest application), linear algebra, and statistics. Since these
fields are used throughout the natural and social sciences, trig is a very useful subject to know.
Astronomy and geography
Trigonometric tables were created over two thousand years ago for computations in astronomy. The
stars were thought to be fixed on a crystal sphere of great size, and that model was perfect for
practical purposes. Only the planets moved on the sphere. (At the time there were seven recognized
planets: Mercury, Venus, Mars, Jupiter, Saturn, the moon, and the sun. Those are the planets that we
name our days of the week after. The earth wasn't yet considered to be a planet since it was the
center of the universe, and the outer planets weren't discovered then.)
The kind of trigonometry needed to understand positions on a sphere is called
spherical trigonometry. Spherical trigonometry is rarely taught now since its job has been
taken over by linear algebra. Nonetheless, one application of trigonometry is astronomy.
As the earth is also a sphere, trigonometry is used in geography and in navigation. Ptolemy (100-178)
used trigonometry in his Geography and used trigonometric tables in his works. Columbus
carried a copy of Regiomontanus' Ephemerides Astronomicae on his trips to the New World and
used it to his advantage.
Engineering and physics
Although trigonometry was first applied to spheres, it has had greater application to planes.
Surveyors have used trigonometry for centuries. Engineers, both military engineers and otherwise,
have used trigonometry nearly as long.
Physics lays heavy demands on trigonometry. Optics and statics are two early fields of physics
that use trigonometry, but all branches of physics use trigonometry since trigonometry aids in
understanding space. Related fields such as physical chemistry naturally use trig.
Mathematics and its applications
Of course, trigonometry is used throughout mathematics, and, since mathematics is applied throughout
the natural and social sciences, trigonometry has many applications. Calculus, linear algebra, and
statistics, in particular, use trigonometry and have many applications in the all the sciences.
On to what is trigonometry
© 1996, 1997.
David E. Joyce
Department of Mathematics and Computer Science
Worcester, MA 01610
Dave's Short Trig Course is located at http://www.clarku.edu/~djoyce/trig