Toán Lớp 11: Y= Cos2x – Sinx +3
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Toán Lớp 11: Y= Cos2x – Sinx +3
Tìm GTLN GTNN
Comments ( 2 )
y = \cos 2x – \sin x + 3\\
y = 1 – 2{\sin ^2}x – \sin x + 3\\
y = – 2{\sin ^2}x – \sin x + 4\\
t = \sin x\left( { – 1 \le t \le 1} \right)\\
\Rightarrow y = f\left( t \right) = – 2{t^2} – t + 4\\
\Rightarrow t = – \dfrac{b}{{2a}} = – \dfrac{1}{4}\\
\Rightarrow f\left( { – \dfrac{1}{4}} \right) = \dfrac{{33}}{8} \Rightarrow \max y = \dfrac{{33}}{8}\\
f\left( { – 1} \right) = 3,f\left( 1 \right) = 1 \Rightarrow \min y = 1\\
\left\{ \begin{array}{l}
\min y = 1 \Rightarrow \sin x = 1\\
\max y = \dfrac{{33}}{8} \Rightarrow \sin x = – \dfrac{1}{4}
\end{array} \right.
\end{array}$