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Strogatz's Nonlinear and Dynamics book states that

$$

\langle\sin^{2n}\rangle = \frac{1\cdot 3\cdot 5\cdots (2n-1)}{2\cdot 4\cdot 6\cdots 2n}

$$

for $n\geq 1$.

However, $\langle\sin^6\rangle = \frac{5}{16}\neq\frac{15}{48}$.

What is the deal here?

$$

\langle\sin^{2n}\rangle = \frac{1\cdot 3\cdot 5\cdots (2n-1)}{2\cdot 4\cdot 6\cdots 2n}

$$

for $n\geq 1$.

However, $\langle\sin^6\rangle = \frac{5}{16}\neq\frac{15}{48}$.

What is the deal here?

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