# Sine and Cosine Project

I have a math project due where the assignment is to find real world applications of the sine and cosine funtions. Can anyone recommend some good websites on the web or have any specific ideas?

Thanks,
-Charlie

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## Answers and Replies

mathman
Science Advisor
Light and sound waves are usually represented as mixtures of sines and cosines.

NateTG
Science Advisor
Homework Helper
One of the most common sine/cosine like movements is that of a piston in an engine or a pump.

virating strings. anything with a rhythmic smooth repetitiveness.

also check out applications of fourier series even though fourier series will probably be beyond the scope of the class, you can see where they are used and say that sine/cosine are used there.

sine/cosine is also used in the rotation of shapes in pictures and graphics such as 3D computer graphics which has nice formulations in 2x2 or 3x3 matricies from linear algebra.

you can also mention how sine/cosine are used to prove what some think of as one of the most beautiful equations ever (attributed to euler):
$$e^{\pi i}=-1$$
from which one can conclude
$$\ln (-1)=\pi i$$

Waves hitting the beach?

A sun dial. That started quite a while ago.

Awsome ideas guys, thanks. Does anyone know where I can find the equations for the different applications?

-Charlie

Simfish
Gold Member
One 'closer to home' approach to trigonometric equations can be in the height of a merry-go-round.

Equations for the trigonometric equations of wavelengths are quite ubiquitous among physics websites; you might just consider running a search on a trigonometric equation for wavelengths, for example.