Final answer:
The 47th derivative of y=sin(x) evaluated at x=π/3 is -√3/2.
Step-by-step explanation:
The problem asks for the 47th derivative of y = sin(x) evaluated at x= π/3. The derivatives of sin(x) follow a periodic pattern with a period of 4. This means that the 1st, 5th, 9th, ... derivatives will all be cos(x), the 2nd, 6th, 10th, ... will be -sin(x), the 3rd, 7th, 11th, ... will be -cos(x), and the 4th, 8th, 12th, ... will be sin(x) again.
To find the 47th derivative, we can divide 47 by 4, which leaves a remainder of 3. This means the 47th derivative will be the same as the 3rd, which is -cos(x). When evaluated at x = π/3,
cos(π/3) = 1/2,
So, the 47th derivative evaluated at π/3 is -1/2.