Question

Determine cos x, sabendo que $\frac{ \pi}{2}$ < x < $\pi$ e sen x = $\frac{3}{5}$

Answer 1

$\sin^{2}x+\cos^{2}=1\\\\ (\dfrac{3}{5})^2+\cos^{2}=1\\\\ \dfrac{9}{25}+\cos^{2}=1\\\\ \cos^{2}=1-\dfrac{9}{25}=\dfrac{25-9}{25}\\\\ \cos^{2}=\dfrac{16}{25}\\\\ \cos x=\pm\sqrt{\dfrac{16}{25}}\\\\ \cos x=\pm\dfrac{4}{5}}$

Como $90^{\circ}$, o cosseno é negativo, então:

$\cos x=-\dfrac{4}{5}}$