For theta in [0, pi],let f(theta) = sin(cos t | vedclass

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(C) Given $f(	heta) = \sin(\cos 	heta)$.$f'(	heta) = -\cos(\cos 	heta) \cdot \sin 	heta$.Since $\cos(\cos 	heta) > 0$ for all $	heta \in [0, \p

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$b < d < a < c$

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(C) Given $f( heta) = \sin(\cos heta)$.$f'( heta) = -\cos(\cos heta) \cdot \sin heta$.Since $\cos(\cos heta) > 0$ for all $ heta \in [0, \pi]$ and $\sin heta \geq 0$ for $ heta \in [0, \pi]$,$f'( heta) \leq 0$.Thus,$f( heta)$ is a decreasing function.$a = f(0) = \sin(1)$ and $b = f(\pi) = \sin(-1) = -\sin(1)$.Given $g( heta) = \cos(\sin heta)$.$g'( heta) = -\sin(\sin heta) \cdot \cos heta$.For $ heta \in [0, \pi/2)$,$\cos heta > 0$ and $\sin(\sin heta) > 0$,so $g'( heta) For $ heta \in (\pi/2, \pi]$,$\cos heta 0$,so $g'( heta) > 0$ (increasing).$c = \max\{g(0), g(\pi)\} = \cos(0) = 1$.$d = g(\pi/2) = \cos(1)$.Since $0 0$.Comparing values: $b = -\sin(1) \approx -0.84$,$d = \cos(1) \approx 0.54$,$a = \sin(1) \approx 0.84$,$c = 1$.Thus,$b < d < a < c$.

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