Why was trigonometry invented?

Answer 1

To solve problems ranging from the simple right-angle triangle that give the 3 basic ratios of Sine, Cosine and Tangent, via surveying and navigation, to the mathematics of such fields as harmonic analysis, vectors, electricity & electronics, etc. Indeed without Trigonometry you would not be able to ask about it on the internet: we would not even have the electricity supply.

One very important point... I have the impression that many 'Answers' users - school pupils I suspect - who regard each field of maths (Trig, Algebra, Calculus etc) as separate academic subjects. They are not: they are all interlinked topics within Mathematics, and there are many real-world problems that require all those 3 example topics in one go. For example, Integrating a harmonic function (in acoustics and electronics, for examples) needs high algebraic skill in order to combine the calculus and the trigonometry and arrive at the correct answer.