Why are the Trig functions so important?

>>8541475
makes working in polar really really easy

good for triggering people

Haha get it? xD

>>8541475
complex numbers = time evolution in waves

>>8541475
Because 90% of math can be drawn.

>>8541475

On the applied side...

Because the basic concept of all of them shows up constantly and unavoidably in surveying land, engineering, construction, etc. Any time you're actually trying to build something, you either need trig or if you've figured out a way to do without it, the truth of the matter is that it still would have been better for you to have hade it, as it would have made your life much easier.

The ancient Egyptians had the seked at least 3500 years ago in connection with their pyramids, and even they were quite bad at math. Yet they sensed that once you get past basic-bitch considerations of number, shape, and basic geometry, one of the next steps is trig. They knew that they needed some way to express relationships involving the sides and angles of right triangles in order to help with building stuff.

On the pure side...

Once they are understood and expressed in their modern forms, the trig functions are an important addition to the family of /elementary functions/, which simply denote functions with which calculus has surprisingly and pleasantly 'nice' results. /It is rather remarkable that the derivative of the sine of x with respect to x is precisely the cosine of x/ etc, and if this no longer impresses you, it's because you're jaded and too far removed from your first exposure to calc. So trig functions also function as important object lessons in how calculus can work in its simplest examples.

Later, trig is implicated in the cartesian plane, later the complex plane, and just behind the scenes in euler's meme-formula and De Moivre's formula.

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>>8541475
Wtf is this OP. Sinus, holy shit that's not a real thing kek

>>8541475
so Suzy can tell Oswald has a hard on always

>>8541475
Like triangles are everywhere man

>>8541475
Because they detail the most basic relationship between a triangle and a circle. As said in this post >>8541820
this relationship comes up so often anytime you're building anything or navigating somewhere that it's practically unavoidable.