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Gaokao Math Practice Question

已知 $\omega>0$, 函数 $f(x)=\sin \left(\omega x+\frac{\pi}{4}\right)$ 在区间 $\left[\frac{\pi}{2}, \pi\right]$ 上单调递减, 则实数 $\omega$ 的取值范围是 ($\qquad $)

  1. A.$\left[\frac{1}{2}, \frac{5}{4}\right]$
  2. B.$\left[\frac{1}{2}, \frac{3}{4}\right]$
  3. C.$\left(0, \frac{1}{2}\right]$
  4. D.$(0,2]$

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