Toán Lớp 11: sin^2 – 4sinx+8 tìm giá trị lớn nhất
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Toán Lớp 11: sin^2 – 4sinx+8 tìm giá trị lớn nhất
Comments ( 1 )
y = f\left( x \right) = {\sin ^2}x – 4\sin x + 8\\
t = \sin x\left( { – 1 \le t \le 1} \right)\\
\Rightarrow y = f\left( t \right) = {t^2} – 4t + 8\\
f\left( 1 \right) = 5,f\left( { – 1} \right) = 13\\
\to \max y = 13 \Rightarrow \sin x = – 1\\
\Rightarrow x = – \dfrac{\pi }{2} + k2\pi \left( {k \in \mathbb{Z}} \right)
\end{array}$