Daniel J Smith Custom TMUA Set A Paper 1 · Question 4

Define functions $g_1$ , $g_2$ , $g_3$ , $g_4$ on the real numbers by

\begin{aligned} g_1(x)&=\sin x\\ g_2(x)&=\sin(\sin x)\\ g_3(x)&=\sin(\sin(\sin x))\\ g_4(x)&=\sin(\sin(\sin(\sin x))) \end{aligned}

Let $M_k$ be the maximum value of $g_k$ for $k=1,2,3,4$

Which one of the following statements is true?

M_1=M_2=M_3=M_4=1

1>M_1>M_2>M_3>M_4>0

1>M_1=M_2=M_3=M_4>0

M_1=1

and

1>M_2>M_3>M_4>0

M_2=M_4

and

M_1=M_3

FNone of the above

examday