a.
\(y=3sinx-\dfrac{1}{2}\)
Do \(-1\le sinx\le1\Rightarrow-3\le3sinx\le3\)
\(\Rightarrow-\dfrac{7}{2}\le3sinx-\dfrac{1}{2}\le\dfrac{5}{2}\)
\(\Rightarrow y_{max}=\dfrac{5}{2}\) ; \(y_{min}=-\dfrac{7}{2}\)
b.
\(y=-5+2sin^32x\)
Do \(-1\le sin2x\le1\Rightarrow-1\le sin^32x\le1\)
\(\Rightarrow-2\le2sin^32x\le2\)
\(\Rightarrow-7\le y\le-3\)
\(y_{max}=-3\) ; \(y_{min}=-7\)
c.
\(0\le cos^2x\le1\Rightarrow3\le cos^2x+3\le4\)
\(\Rightarrow-2\le-\sqrt{cos^2x+3}\le-\sqrt{3}\)
\(\Rightarrow-5\le y\le1-3\sqrt{3}\)
\(y_{min}=-5\) ; \(y_{max}=1-3\sqrt{3}\)
d.
Do tính chất căn thức ta có \(\sqrt{2+3sinx}\ge0\)
\(sinx\le1\Rightarrow3sinx\le3\Rightarrow2+3sin\le5\)
\(\Rightarrow3\le y\le3+\sqrt{5}\)
\(y_{min}=3\) ; \(y_{max}=3+\sqrt{5}\)
