How do you find the taylor series for #sinx# in powers of #x-pi/4#?
According to the definition of Taylor series it should be
Now you have to compute the first derivatives at
You will see a pattern to arise which is periodic.
Finally (if my calculations are right) you should find tht the Taylor pattern is
The "strange" bracket sign you see in the formula above is the integer part or floor function
See the definition for Taylor series and integer part function