1. Consider the function f(x) := sin(x). (a) Give the Taylor polynomial P6(x) of degree 6 about a = 7/6 of this function. Note: use the exact values of sin(7 /6) = 1/2 and cos(7 /6) = V3/2. (b) Give the nested representation of the polynomial Q6(t) := P6(x(t)) where t := x - 7/6 (x(t) = t+1/6). (c) Using the nested multiplication method (also called Horner's algorithm), compute the approximation P6(0.6) to sin(0.6) (give at least 15 significant digits of P6(0.6)) (d) Without using the exact value of sin(0.6), but using the bounds 0.5