I do not know about the sinus values in embedded processors, since pre-computed values can be used. The principal problem with the interpolation with the cardinal series is that it is highly, one could even say extremely, acausal. To correctly implement it, you have to go back to times before the big bang and forward to the times after the dissolution of our galaxy to obtain the samples required for an exact reconstruction, and who in these days has that time and money.
So you always use filters that are imperfect from the theoretical point of view. To account for that gap between ideal theory and real practice, one uses a sampling frequency that is a higher multiple of the highest frequency in the signal than just the Nyquist double. Humanly perceptible sound goes to 12kHz according to vinyl and to 15kHz according to CDs and mp3. The range from 41-48kHz provides a safe multiple of
3 2.5-4 of the frequency range.
Please note "according to vinyl ... and mp3", which means that recordings of widely acceptable quality are produced with filtering the sound down to the frequency band limit of 12kHz-14kHz and thus having an oversampling factor of 3-4 when encoding with 41-48kHz. People trained in listening to orchestral music may notice the missing harmonics, especially at solos of high-pitched instruments.