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Trigonometric identities happen to be invented for triangles: sin, cosine and through them tangent.

Later at school I learnt that they are periodic and have wave appearance. Than in University I came across a new topic, the Fourier series that depends on sin and cosine. At the end I was exposed to Fourier transform and how than DFT and how central it is to the communication theory.

--> My question is this, and I REALLY want a big answer to it since I have thought about it for some years. If mankind had not developed trigonometric ratios for triangles, we would not have fourier series and fourier transform (originally a method for the heat differential equation) and thus not have concept of frequency spectrum. Would it also mean that the wave equation would not exist? In terms of the advancement mankind has made e.g through frequency analysis, communication systems and radars, telephones and internet and much more. Would all this not have developed if trigonometric rations did not exist?

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closed as not constructive by Leon Heller, Chris Stratton, placeholder, Dave Tweed, Olin Lathrop Mar 25 '13 at 20:41

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance. If this question can be reworded to fit the rules in the help center, please edit the question.

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    \$\begingroup\$ This question isn't a very good fit for this site. It's not really clear if you are asking about the math or the physical laws which it models, but regardless it is more a question of philosophy than of engineering. \$\endgroup\$ – Chris Stratton Mar 25 '13 at 19:41
  • \$\begingroup\$ OK I will summarize my question. A lot of what we have developed today comes from the communications theory which gave a big push to electronics itself. If trig ratios did not exist, will all this science and technology depending on communications theory be around? \$\endgroup\$ – quantum231 Mar 25 '13 at 20:00
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    \$\begingroup\$ It still doesn't have anything to do with electronic design. \$\endgroup\$ – Leon Heller Mar 25 '13 at 20:20
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    \$\begingroup\$ Any answer would be pointless speculation at best, since there would be no way to prove or disprove it. We are where we are, we can't go back and re-run history to see how things might be different. Move along. \$\endgroup\$ – Olin Lathrop Mar 25 '13 at 20:43
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    \$\begingroup\$ Actually the assumption in the question is wrong. The earliest radio communication consisted of using sparks to generate random hash that propagated through space, and crude detectors. Nothing to do with nice sine waves. \$\endgroup\$ – Kaz Mar 26 '13 at 4:56
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We did not invent trigonometric ratios. They were already there, and we simply discovered them. I hope you aren't proposing a world where trig didn't actually work. I have no answer for that.

What you will find is that all of these observations and methods are interrelated. Every time you learn of a new method, you will find parts of other methods being used. Sometimes you'll find the same thing, but done another way.

If we didn't have trigonometry, we would have discovered it after working on the other problems.

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Human have had a innate understanding of frequency for a long time, probably since Caveman days. Even today, other animals understand the rising and falling pitch of bird calls and whale songs. None of these had Fourier transforms.

The cool thing about science is that it does not rely on your belief, faith, or your understanding for it to work.

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