Question

$Ştiind \: că : \: sinx = \frac{3}{5} ,x \: \in \: ( \frac{\pi}{2} ;\pi)$

$Să \: se \: calculeze \: cosx.$

Answer 1

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