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[tex]Ştiind \: că : \: sinx = \frac{3}{5} ,x \: \in \: ( \frac{\pi}{2} ;\pi)[/tex]

[tex]Să \: se \: calculeze \: cosx.[/tex]


Răspuns :

[tex]Formula fundamentala a trigonometriei: sin^{2} x+cos^{2}x=1\\Deci cos^{2}x=1-sin^{2}x\\\\sin x = \frac{3}{5}  => sin^{2}x=\frac{9}{25} \\cos^{2}x=1-\frac{9}{25}=\frac{25-9}{25} =\frac{16}{25} \\cosx=\sqrt[]{\frac{16}{25} } =\frac{4}{5}[/tex]