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Mathematics
Mathematics
Problem
For
f
(
x
)
=
sin
x
f(x)=\sin x
f
(
x
)
=
sin
x
, which of the following best describes
f
(
n
)
(
x
)
f^{(n)}(x)
f
(
n
)
(
x
)
for every integer
n
≥
0
n\ge 0
n
≥
0
? a)
cos
(
x
+
n
π
2
)
\cos\bigl(x+\tfrac{n\pi}{2}\bigr)
cos
(
x
+
2
nπ
)
b)
sin
(
x
+
n
π
)
\sin\bigl(x+n\pi\bigr)
sin
(
x
+
nπ
)
c)
sin
(
x
+
n
π
2
)
\sin\bigl(x+\tfrac{n\pi}{2}\bigr)
sin
(
x
+
2
nπ
)
d)
{
sin
x
,
n
even
cos
x
,
n
odd
\begin{cases}\sin x,& n\text{ even}\\ \cos x,& n\text{ odd}\end{cases}
{
sin
x
,
cos
x
,
n
even
n
odd
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