Recall that we found in Preview 8.2.1 and subsequent work that sin(x)~~x-(1)/(3!)x^(3)+(1)/(5!)x^(5)-(1)/(7!)x^(7), which is the degree 7 Taylor approximation centered at 0. And in Activity 8.2.2, we found that the degree 6 Taylor approximation centered at a=0 for cos(x) is cos(x)~~1-(1)/(2!)x^(2)+(1)/(4!)x^(4)-(1)/(6!)x^(6). In this exercise, we investigate Taylor polynomial approximations of f(x)=sin(x) centered at a=(\pi )/(2). a. By finding the appropriate derivatives of f(x)=sin(x) and evaluating them at a=(\pi )/(2), determine the degree 6 Taylor polynomial approximation of sin(x) centered at a=(\pi )/(2). b. How is your result in (a) similar to the degree 6 Taylor polynomial of cos(x) that is centered at a=0? c. Recall the trigonometric identity that states sin(x)=cos(x-(\pi )/(2)). How does this identity help explain what you found in (a) and (b)?