The functions $f _ { 1 }$ to $f _ { 5 }$ are defined on the real numbers by
$$\begin{aligned} & \mathrm { f } _ { 1 } ( x ) = \cos x \\ & \mathrm { f } _ { 2 } ( x ) = \sin ( \cos x ) \\ & \mathrm { f } _ { 3 } ( x ) = \cos ( \sin ( \cos x ) ) \\ & \mathrm { f } _ { 4 } ( x ) = \sin ( \cos ( \sin ( \cos x ) ) ) \\ & \mathrm { f } _ { 5 } ( x ) = \cos ( \sin ( \cos ( \sin ( \cos x ) ) ) ) \end{aligned}$$
where all numbers are taken to be in radians. These functions have maximum values $m _ { 1 } , m _ { 2 } , m _ { 3 } , m _ { 4 }$ and $m _ { 5 }$, respectively. Which one of the following statements is true?
A $m _ { 1 } , m _ { 2 } , m _ { 3 } , m _ { 4 }$ and $m _ { 5 }$ are all equal to 1
B $0 < m _ { 5 } < m _ { 4 } < m _ { 3 } < m _ { 2 } < m _ { 1 } = 1$
C $\quad m _ { 1 } = m _ { 3 } = m _ { 5 } = 1$ and $0 < m _ { 2 } = m _ { 4 } < 1$
D $m _ { 1 } = m _ { 3 } = m _ { 5 } = 1$ and $0 < m _ { 4 } < m _ { 2 } < 1$
E $m _ { 1 } = m _ { 3 } = 1$ and $0 < m _ { 2 } = m _ { 4 } < 1$ and $0 < m _ { 5 } < 1$ F $m _ { 1 } = m _ { 3 } = 1$ and $0 < m _ { 4 } < m _ { 2 } < 1$ and $0 < m _ { 5 } < 1$