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Mathematics
Mathematics
Problem
For the function
f
(
x
)
=
sin
x
f(x)=\sin x
f
(
x
)
=
sin
x
, successive derivatives exhibit a repeating pattern. a. Derive a general expression for
f
(
n
)
(
x
)
f^{(n)}(x)
f
(
n
)
(
x
)
, where
n
n
n
is a positive integer. b. Using your result from part (a), determine the exact value of
f
(
37
)
(
π
6
)
f^{(37)}\!\left(\dfrac{\pi}{6}\right)
f
(
37
)
(
6
π
)
.
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