So you have a sine/cosine pair of signals from an encoder, and you want to generate a 2nd pair of sine/cosine signals from those with a known phase-shift. The encoder frequency varies. You don't state if you need the encoder to work in both directions?

Assuming you want a digital solution and a predictable lag, and a small amount noise/error was acceptable then:

1. ADC both analog sine/cosine signals simulataneously.

2. Extract quadrant (if it's 0-90, 90-180, 180-270, 270-0) and direction - you'll need the cosine for this unless you track the previous conversion.

3. Throw the sine (adjusted for 0-90) against a big LUT - this will extract convert SINE to DEGREES.

4. Add/subtract your OFFSET DEGREES to create new sine and cosine angles in degrees

5. Throw both against another big LUT to create your new output SINE and COSINE, adjust for quadrant.

6. Wack out the numbers using DACS.

I've done very successfully used LUT's with interpolation to get manageable LUT size and very high resolution. It's not rocket-science, but you will need to draw this out carefully, it's lots of little steps. If you don't need speed, then you can probably do the maths in a small micro - but LUT's are cheap and simple.