Question

Tìm TXĐ của hệ số lượng giác sau: \(y=\sqrt{5\sin x-1}+2\)

Answer 1

\(Vì-1\le\sin x\le1\)

\(\Rightarrow-5\le5\sin x\le5\)

\(\Rightarrow-6\le5\sin x-1\le4\)

Vì \(5\sin x-1\ge0\Leftrightarrow\sin x\ge\dfrac{1}{5}\)

\(\Rightarrow\sqrt{\dfrac{1}{5}}\le\sqrt{5\sin x-1}\le\sqrt{4}\)

\(\Rightarrow\dfrac{1}{\sqrt{5}}\le\sqrt{5\sin x-1}\le2\)

\(\Rightarrow\dfrac{1}{\sqrt{5}}+2\le\sqrt{5\sin x-1}+2\le4\)

\(\Rightarrow\dfrac{1}{\sqrt{5}}+2\le y\le4\)

\(Vậy\) \(y_{max}=4\)

        \(y_{min}=\dfrac{1}{\sqrt{5}}+2\)

 

Answer 2

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