TMUA 2022 Paper 2 Q20 — Worked Solution

P2·Trigonometry, Functions, Transformations & Graphs·7.5Official · 2022 · Q20

nested-trigmaximum-valuecomposition

The functions

f_{1}

f_{5}

are defined on the real numbers by

f_{1} (x) f_{2} (x) f_{3} (x) f_{4} (x) f_{5} (x) = cos x = sin (cos x) = cos (sin (cos x)) = sin (cos (sin (cos x))) = cos (sin (cos (sin (cos x))))

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?

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