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Consider the equation $f(x)=\cos \left(x+\frac{\pi}{2} \right)$. What is the average rate of change on the interval $\left[-\cfrac{\pi}{2}, b \right]$?

A

$\cfrac{b+\cfrac{\pi}{2}}{1-\cos \left(b+\cfrac{\pi}{2} \right)}$

B

$\cfrac{1-\cos \left(b+\cfrac{\pi}{2} \right)}{b+\cfrac{\pi}{2}}$

C

$\cfrac{\cos \left(b+\cfrac{\pi}{2} \right)-\cos(b)}{b+\cfrac{\pi}{2}}$

D

$\cfrac{\cos \left(b+\cfrac{\pi}{2} \right)-1}{b+\cfrac{\pi}{2}}$

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