Question

Find the maximum value of $f(x) = sin(sinx)$ for all $x \in R$

• A. $-sin \,1$
• B. $sin \,6$
• C. $sin \,1$
• D. $-sin \,3$

Answer 1

Answer: (C)

$sin \,1$

Answer 2

We have $f(x) = sin\,(sin\,x)$, $x \in R$ Now, $-1 \le sin \,x \le 1$ for all $x \in R$ $\Rightarrow sin \left(-1\right) \le sin\left(sinx\right) \le sin \,1$ for all $x \in R$ [$\because sin\, x$ is an increasing function on $\left[-1,1 \right]$] $\Rightarrow - sin\, 1 \le f\left(x\right) \le sin\, 1$ for all $x \in R$ This shows that the maximum value of $f\left(x\right)$ is $sin \,1$.