Practical uses of trig functions

Question

What are some practical applications of sine, cosine, arc sine, etc.

Can you distort images, calculate special values, or other stuff?

Any opinions of the most used/important?

Answer 1

• Almost any graphic manipulations that invlove rotations both on plane (2D) as well as in 3D space.
• Planning trajectories of robotic arms
• Adjusting connection weights in neural networks
• Creating fractals (and other fancy shapes)
• Implementing control algorithms for industrial controllers

and more and more and more

Answer 2

Well, to start, anything tagged with trigonometry definitely uses those functions. Functions that work with positioning stuff on the screen (which is, after all, an X-Y plane of pixel coordinates) could end up using them to position objects or tilt them at angles. Geographical applications will definitely need them to represent paths which don't go straight east-west or north-south.

The most important that I can think of, though, is signal processing which involves heavy use of trig functions in conversions to Fourier series (indeed, a Fourier Transformation is a change to representing a signal only with sine and cosine). The Fourier transformed representation of a signal that can often be more convenient, and sometimes is actually the only way to find properties from signals. Signal processing has applications in graphics, the structure of the internet, audio applications, speech-to-text or text-to-speech, scientific data sensor programs... the list is nearly endless.

Answer 3

First of all, what do you mean by "graphing functions"? Given a function f, you can create its graph { (x, y), y=f(x) }. Anyway, these functions are extremely fundamental to mathematics, physics, chemistry, biology, etc., etc., and so they appear everywhere. In particular, any function can be used to distort images and to make cool special effects (either you can transform spatial coordinates, or you can transform colour values in RGB, HSL, or HSV). Special effects propably make up 0.0001 % of all applications of the trigonometric functions.

My point is, since these functions are so fundamental to every branch of science, it would be impossible to enumerate a few practical applications alone. (But if you start with Mchl's list and add a few million other items, then you will probably get pretty close.)

To try to see this, we can think of a simpler mathematical operation: division. One might ask: I know that I can use division to divide a cake equally to all guests at my party. But can I use division for anything else?

Yes, you can:

• If you divide the number of bits by the bitrate (number of bits per second) of an audio stream, you get the duration (in seconds) of the stream.

• If you divide the energy of a photon by Planck's constant, you get the frequency of the light (radiation).

• If you divide the force on an electron in an electric field by its charge, you get the field strength.

• ...

In this case, a million other items would not be enough to cover what scientists are working with daily. Nevertheless, I hope this makes my point clear: fundamental mathematical operations (functions, ideas) can be applied to every branch of science, and therefore they are virtually omnipresent.