Câu 28:
\(sinx-cosx=\dfrac{\sqrt{2}}{3}\cdot m\)
=>\(\sqrt{2}\cdot sin\left(x-\dfrac{\Omega}{4}\right)=\dfrac{\sqrt{2}}{3}\cdot m\)
=>\(sin\left(x-\dfrac{\Omega}{4}\right)=\dfrac{m}{3}\)
Để phương trình có nghiệm thì \(-1< =\dfrac{m}{3}< =1\)
=>-3<=m<=3
Câu 29:
\(-1< =sinx< =1\)
=>\(-3< =3\cdot sinx< =3\)
=>\(-3-2+m< =3\cdot sinx-2+m< =3-2+m\)
=>\(m-5< =y< =m+1\)
Để \(y_{min}=-10\) thì m-5=-10
=>m=-5
29.
\(3sinx-2+m\ge3.\left(-1\right)-2+m=m-5\)
\(\Rightarrow m-5=-10\)
\(\Rightarrow m=-5\)
30.
\(y=2\left(2cos^2x-1\right)-3cosx-5-m\)
\(=4cos^2x-3cosx-7-m\)
\(=\left(cosx+1\right)\left(4cosx-7\right)-m\)
Do \(-1\le cosx\le1\Rightarrow\left\{{}\begin{matrix}cosx+1\ge0\\4cosx-7< 0\end{matrix}\right.\)
\(\Rightarrow\left(cosx+1\right)\left(4cosx-7\right)\le0\)
\(\Rightarrow y\le-m\Rightarrow y_{max}=-m\)
\(\Rightarrow-m=9\Rightarrow m=-9\)
27.
\(sinx.cosx=2m+7\)
\(\Leftrightarrow2sinx.cosx=2\left(2m+7\right)\)
\(\Leftrightarrow sin2x=2\left(2m+7\right)\)
Pt có nghiệm khi \(-1\le4m+14\le1\)
\(\Rightarrow-\dfrac{15}{4}\le m\le-\dfrac{13}{4}\)
28.
\(sinx-cosx=\dfrac{\sqrt{2}}{3}m\)
\(\Leftrightarrow\sqrt{2}sin\left(x-\dfrac{\pi}{4}\right)=\dfrac{\sqrt{2}}{3}m\)
\(\Leftrightarrow sin\left(x-\dfrac{\pi}{4}\right)=\dfrac{m}{3}\)
Pt có nghiệm khi:
\(-1\le\dfrac{m}{3}\le1\Rightarrow-3\le m\le3\)
