\({\rm{sin }}{49^o},{\rm{ cos }}{15^o},{\rm{ sin }}{65^o},{\rm{ cos }}{50^o},{\rm{ }}\cos {\rm{ }}{42^o}\) A \(\sin {49^0} < \sin {65^0} < \cos {15^0} < \cos {50^0} < \cos {42^0}\) B \(\cos {50^0} < \cos {42^0} < \sin {49^0} < \sin {65^0} < \cos {15^0}\) C \(\cos {50^0} < \cos {42^0} < \cos {15^0} < \sin {49^0} < \sin {65^0}\) D \(\cos {15^0} < \cos {42^0} < \cos {50^0} < \sin {49^0} < \sin {65^0}\)

\({\rm{sin }}{49^o},{\rm{ cos }}{15^o},{\rm{ sin }}{65^o},{\rm{ cos }}{50^o},{\rm{ }}\cos {\rm{ }}{42^o}\)

A \(\sin {49^0} < \sin {65^0} < \cos {15^0} < \cos {50^0} < \cos {42^0}\)

B \(\cos {50^0} < \cos {42^0} < \sin {49^0} < \sin {65^0} < \cos {15^0}\)

C \(\cos {50^0} < \cos {42^0} < \cos {15^0} < \sin {49^0} < \sin {65^0}\)

D \(\cos {15^0} < \cos {42^0} < \cos {50^0} < \sin {49^0} < \sin {65^0}\)

Hướng dẫn Chọn đáp án là: B

Phương pháp giải:

Áp dụng \(0 < \alpha < \beta < {90^0} \Rightarrow \left\{ \begin{array}{l}\sin \alpha < \sin \beta \\cos\alpha > cos\beta \end{array} \right..\)

Ta có: \(\alpha + \beta = {90^0} \Rightarrow \left\{ \begin{array}{l}\sin \alpha = \cos \beta \\\cos \alpha = \sin \beta \end{array} \right.\)

Lời giải chi tiết:

\({\rm{sin }}{49^o},{\rm{ cos }}{15^o},{\rm{ sin }}{65^o},{\rm{ cos }}{50^o},{\rm{ }}\cos {\rm{ }}{42^o}\)

Ta có: \(\left\{ \begin{array}{l}sin{\rm{ }}{49^0} = \cos {\rm{ }}\left( {{{90}^0} – {{41}^0}} \right) = {\rm{sin 4}}{{\rm{1}}^0}\\sin{\rm{ 6}}{{\rm{5}}^0} = \cos {\rm{ }}\left( {{{90}^0} – {{25}^0}} \right) = {\rm{sin 2}}{{\rm{5}}^0}\end{array} \right.\)

Vì \({15^0} < {25^0} < {41^0} < {42^0} < {50^0}\)\( \Rightarrow \cos {\rm{ }}{50^o} < \cos {\rm{ }}{42^o}{\rm{ < }}\cos {\rm{ 4}}{{\rm{1}}^o}{\rm{ < }}\cos {\rm{ 2}}{{\rm{5}}^o} < \cos {15^0}\)

\( \Rightarrow {\rm{cos }}{50^0} < \cos {\rm{ }}{42^0} < {\rm{sin }}{49^0} < {\rm{sin }}{65^0}{\rm{ < cos }}{15^0}\)

Chọn B.