Why is Trigonometry used in so many applications that have nothing to do with triangles?
In: Mathematics
While the origin of the word relates to angles and measures of a triangle, it is probably more useful to think of a triangle as the simplest polygon and that an “extreme” form of regular polygons, ie with the “most” sides, is the circle.
In that sense, the subject develops naturally to the study of circles and of particular importance in the real world, circular motion. With the further development in mathematics, it has been shown that any closed shape can be inscribed as a series of circular motions of circles of various shapes (although the number of circles might be very large to the extent of requiring an infinity of circles).
The other property of circular motion is that it is periodic (ie it eventually repeats). This is very useful for the analysis of periodic motion – the simplest being what many people think of as “waves”. Waves appear to be a very fundamental property of the universe (light waves, sound waves, radio waves etc etc) So the mathematics of trigonometry lead to circles and circular motion and then to waves and periodic motion in general. It becomes foundational to nearly all physics and engineering.
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