Usage of Digital Cosine Transform in lossy compression of images
A rectangular window of data can have a discontinuity between the front and back edge.  An FFT of that window represents that circular edge discontinuity with energy in a bunch of high frequency bins.  Take that segment of signal and mirror it around one edge.  Note that a circular or periodic extension of this no longer has a discontinuity across the edge.  The FFT of that doubled-by-mirroring signal might thus have less information energy in the high bins.  Thus there may be more of these high bins that can be "thrown away" by a compression algorithm without major damage (information loss).

A DCT is an FFT of the doubled-by-mirroring product.  Since the mirrored intermediate vector is symmetric, some efficiency can be gotten by throwing away any computations only required for the sine components since they will be zero anyway.

A DST would be the FFT of a doubled-by-mirroring-the-inverse signal, which would make the discontinuities worse, which would spread even more information/energy into the bins you would really like to throw away, thus making things far worse for simply but lossy compression.