Trigonometry is important to mathematics as an element of calculus, statistics and linear algebra. Outside of mathematics, it is important to physics, engineering, geography and astronomy as well as architectural design.
Trigonometry is a fundamental component of calculus. In statistics, trigonometric functions are necessary for the computation of the bell curve and for the study of seasonal periodicities. Most uses of trigonometry in other fields relate to the use of Fourier series, which cannot be calculated without the use of trigonometry.
A wide range of nonmathematical fields rely on trigonometric functions, even if members of those fields are not aware that trigonometry is involved. Aside from those already mentioned, trigonometry has contributed to advances in the fields of acoustics, architecture, cartography, civil engineering, geophysics, crystallography, electronics, medical imaging and pharmacology. Spherical trigonometry was used in astronomy to compute the location of stars and planets prior to the invention of linear algebra. Surveyors and engineers have been using trigonometry in their work for hundreds of years.
Common practical, modern applications of trigonometry include its use in satellite navigation, naval and aviation industries, the composition of music, and all types of digital imaging. It has also become critical in the construction of modern buildings.