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Is there anything cool about trigonometry? I was just curious. I'm learning trig right now and I often find myself asking myself, "What's the point?" I feel if I knew what I was working on and why, I'd be more successful and goal-oriented.

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See amazon.com/gp/aw/d/0691158207/… and the even cooler amazon.com/gp/aw/d/… –  symplectomorphic Jul 11 at 0:33
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After reading the first sentence I was going to downvote. I only resisted from this when I saw two downvotes already present (likely for similar reasons). Why downvote? The first sentence somewhat insulted me by supposing there has to be "something" cool in a thing which is cool by itself. Please consider rephrasing. –  Ruslan Jul 11 at 10:44
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@Ruslan Without trigonometry the OP were not able to use a computer to write that sentence. You are quite right. Lanczos said that it will save just Fourier stuff if the world is going to an end. –  Felix Marin Jul 11 at 20:43

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Want to build something with tools? You'll need trig to get the measurements right. Want to create a game? You'll need trig to understand the math. Want to work with electronics? You'll need trig to understand all sorts of things Want to do astronomy? You'll need physics which uses LOTS of trig. Want to pass high school and get into a college STEM course? You'll need trig.

At its core Trig is pretty simple, and its all about triangles, and how the lengths of sides and the angles work together. From that all the other good stuff emerge, like how circles work , which leads to how sine/cosine waves work, which then gives you magic stuff like the Fourier series which explains how signals work and pretty much all of modern technology.

Don't be put off by all the cos/cos/tan stuff. Its really easy to understand! Its probably the most fun part of maths I can think of, well maybe group theory is, but I think your a few years off that lol.

Heres the secret sauce: If your teacher gives you something you can't understand. Try asking him to draw an illustration of it.

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I have always been intrigued by the fact that $\sin$ and $\cos$ appear "automatically" if you put an imaginary number into the power series of the $e^x$.

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an interesting physics/engineering application is damping. see en.wikipedia.org/wiki/…. overdamped and undamped systems oscillate (which involve trigonometric functions), but critically and over damped systems (which involve exponential functions) do not oscillate. –  John Joy Jul 11 at 13:42

Trigometry is at the core of (Euclidean) geometry. Any shape you can describe using lengths and angles, you can calculate exact positions/co-ordinates on it using trigonometry.

So, if an architect says "Let's put a rectangle in the middle, at an angle so its corners touch these edges", then trigonometry is the thing that tells them the actual distances they need to specify to make it work.

Want to make a fancy optical illusion with reflections and so on where everything lines up? Your options are days of trial and error, or a simple diagram and some trig.

Doing some DIY in an odd-shaped old house and want to know if this bookcase will fit onto this angled wall? Trig is more reliable than intuition.

It could be that you forget it all before you ever get to a stage where DIY stores are relevant - but if you can remember it (especially if no-one else can) then you'll basically be a wizard.


For the nerds: The "trigonometric functions" themselves (sin/cos/tan/etc.) end up being very useful outside of geometry as well. Further on (calculus and dynamic systems), we see that all sorts of very simple physical setups end up resonating using sine/cos curves - objects on a spring, simple circuits, etc. If you ever want to even vaguely understand how mp3 encoding works, you'll find that sine-waves are essential to the Fourier transform that powers it.

However, the future promises of trigonometry might not be enticing to some, particularly if they're finding it hard to be interested in mathematics now. But the extra joy is there if you reach it. :)

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Trigonometry is the door to periodic functions, a class of functions that have many very curious properties. Some introductions begin by talking about an unmotivated rotating unit vector; but I think it's much more sensible to begin with the relationships among the sides and angles of right triangles, then extend it to all angles, positive and negative.

Many curious questions arise involving the trigonometric functions. I had no idea how interesting trigonometry was until long after I had the course. Now, over sixty years later I still think the questions are interesting. Decades ago I thought about how one could uniquely catalog ALL trigonometric identities. I had a number of ideas but I didn't follow through. I still wonder what can be done, as well as answers to other questions.

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