3 b) Show that the function given by f (x) = \sin x is

decreasing in \left ( \frac{\pi}{2},\pi \right )

Answers (1)

f(x) = sin x
f^{'}(x) = \cos x
Since,  \cos x < 0  for each x \ \epsilon \left ( \frac{\pi}{2},\pi \right )
So, we have    f^{'}(x) < 0
Hence, f(x) = sin x is strictly decreasing in \left ( \frac{\pi}{2},\pi \right )

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