A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. DCTs are important to numerous applications in science and engineering, from lossy compression of audio (e.g. MP3) and images (e.g. JPEG) (where small high-frequency components can be discarded), to spectral methods for the numerical solution of partial differential equations.
The use of cosine rather than sine functions is critical in these applications: for compression, it turns out that cosine functions are much more efficient, whereas for differential equations the cosines express a particular choice of boundary conditions.
References: Wikipedia contributors, "Discrete sine transform," Wikipedia, The Free Encyclopedia, available at: http://en.wikipedia.org/w/index.php?title=Discrete_sine_transform K. R. Castleman, Digital Image Processing. Chapter 13, p.288. Prentice. Hall, 1998.