3. (a) Find the 5th order Taylor polynomial about a = 7r for sin 2:. 1_11r - (b) Use this Taylor polynomial to approximate sin 12 1n terms of powers of 112 (c) The remainder term for a polynomial of order n expanded about gr = a is (IE _ a)'n+1 RM 2 f (71%) (71+ 1)! where 6 lies between a and .161 Write down the remainder term for the polynomial that you have found in part (a). (d) Use the remainder term that you have found in part (c ) to show that theTaylor polynomial approximation to sin 111\" that you found 1n part (b) is within 106 of the actual value of 5111117r Use your 2calculator to verify that the difference between 12 sin 11\" and your approximation is indeed less than 10 6