Calculus -Trignonometry

Question

Find f''(pi) given f(x)=(-1/2)sin(pi -3x)

Answer 1

This answer can be shown leaving sin as expressed or by first noting that

sin(π - 3x) = sin(π) cos (-3x) + cos(π)sin(-3x) = 0 cos(3x) + (-1)(-sin(3x)) = sin(3x)

Then, (-1/2 sin(3x))'' = (-3/2 cos(3x))' = 9/2 sin(3x)

Then, f''(π) = 9/2 sin(3x) = 9/2 sin(3π) = 0