[tex]\displaystyle\bf\\x\in\left(\frac{3\pi}{2},~2\pi \right)\\\\x~este~in~cadranul~~4\\\\In~cadranul~4~cosinusul~este~pozitiv~iar~sinusul~este~negativ.\\\\cos\,x=\frac{4}{5}\\\\sin\,x=\pm\sqrt{1-cos^2x}\\\\\textbf{Formula are }\pm\textbf{ in fata radicalului, dar noi alegem semnul}\\\textbf{in functie ce cadranul in care suntem.}\\\\[/tex]
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[tex]\displaystyle\bf\\sin\,x=\pm\sqrt{1-cos^2x}\\\\sin\,x=\pm\sqrt{1-\left(\frac{4}{5}\right)^\b2}}\\\\\\sin\,x=\pm\sqrt{1-\frac{16}{25}}\\\\\\sin\,x=\pm\sqrt{\frac{25-16}{25}}\\\\\\sin\,x=\pm\sqrt{\frac{9}{25}}\\\\\\\textbf{Alegem semnul minus deoarece}\\\textbf{sinusul este negativ in cadranul 4}\\\\\boxed{\bf~sin\,x=-\frac{3}{5}}[/tex]
