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Using linear approximation methods, approximate $\sin\left(\dfrac{5\pi}{16}\right)$.

$\dfrac{\sqrt{2}}{2}+\dfrac{\sqrt{2\pi}}{32}$

$\dfrac{\sqrt{3}}{2}-\dfrac{\pi}{96}$

$\dfrac{\sqrt{3}}{2}-\dfrac{\pi}{48}$

$\dfrac{1}{2}-\dfrac{\pi}{96}$