4. (2+2 points) (a) Use Taylor's Inequality to bound the error in using the Taylor polynomial from 3(a) to estimate sin(3) (you may keep 7r in your answer). (b) You may notice that your error is still fairly large, since 37\" is pretty far from El. Suppose we wish to use a larger Taylor polynomial: what is the smallest n so that approximating sin(33") using the degree to Taylor polynomial of sin centered at 12; gives a guaranteed error of less than E by Taylor's Inequality? Note: you may use a 4-function calculator for this part (apprmcimating 7r by 3.14 will be close enough for this purpose). Trialand-error will work pretty quickly if your setup is correct