7: \(\Omega< x< \dfrac{3}{2}\Omega\)
=>\(sinx< 0\)
\(\Omega< x< \dfrac{3}{2}\Omega\)
=>\(2\Omega< 2x< 3\Omega\)
=>\(sin2x>0\)
\(sin^2x+cos^2x=1\)
=>\(sin^2x+\left(-\dfrac{5}{13}\right)^2=1\)
=>\(sin^2x=\dfrac{144}{169}\)
mà sin x<0
nên \(sinx=-\sqrt{\dfrac{144}{169}}=-\dfrac{12}{13}\)
\(sin2x=2\cdot sinx\cdot cosx=2\cdot\dfrac{-5}{13}\cdot\dfrac{-12}{13}=\dfrac{120}{169}\)
\(cos2x=2\cdot cos^2x-1=2\cdot\left(-\dfrac{5}{13}\right)^2-1=2\cdot\dfrac{25}{169}-1=\dfrac{50}{169}-1=-\dfrac{119}{169}\)
\(tan2x=\dfrac{sin2x}{cos2x}=\dfrac{120}{169}:\dfrac{-111}{169}=-\dfrac{120}{111}\)
8: \(\dfrac{3}{4}\Omega< x< \Omega\)
=>\(\dfrac{3}{2}\Omega< 2x< 2\Omega\)
=>\(cos2x>0\)
\(cos^22x+sin^22x=1\)
=>\(cos^22x=1-sin^22x=1-\left(-\dfrac{4}{5}\right)^2=\dfrac{9}{25}\)
mà cos2x>0
nên \(cos2x=\dfrac{3}{5}\)
\(\dfrac{3}{4}\Omega< x< \Omega\)
=>\(cosx< 0;sinx>0\)
\(cos2x=2cos^2x-1\)
=>\(2\cdot cos^2x-1=\dfrac{3}{5}\)
=>\(cos^2x=\dfrac{4}{5}\)
mà cosx<0
nên \(cosx=-\sqrt{\dfrac{4}{5}}=-\dfrac{2\sqrt{5}}{5}\)
\(sin^2x+cos^2x=1\)
=>\(sin^2x=1-\dfrac{4}{5}=\dfrac{1}{5}\)
mà sin x>0
nên \(sinx=\sqrt{\dfrac{1}{5}}=\dfrac{\sqrt{5}}{5}\)
\(tanx=\dfrac{sinx}{cosx}=\dfrac{\sqrt{5}}{5}:\dfrac{-2\sqrt{5}}{5}=\dfrac{-1}{2}\)
