Why is Trigonometry used in so many applications that have nothing to do with triangles?
In: Mathematics
The first lie they teach you about trigonometry is that it comes from triangles. Trigonometry comes from properties of circles and the triangle stuff is just one useful application (if it came from triangles, then expressions like sin(190°) or cos(5pi/4) would not make any sense, since triangles can’t have angles that big). Circles in turn provide a very nice example of periodic motion: Going around a circle one and a half times puts me in the same place as going around it halfway, or two hundred sixty nine and a half times. If we for example want to understand something periodic but more complicated, then you can break it down as a sum of a bunch of sin and cos functions which is easier to analyse than a very complex expression.
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