Question

determine o cos x sabendo que 

$\frac \pi 2 < x < \pi e sen x = \frac{3}{5}$

Answer 1

Pela fórmula ($\sin^{2}(\theta)+\cos^{2}(\theta)=1$), podemos descobrir $\cos x$:

$\sin^{2}x+\cos^{2}x=1$

$\left(\dfrac{3}{5}\right)^{2}+\cos^{2}x=1$

$\dfrac{9}{25}+\cos^{2}x=1$

$\cos^{2}x=1-\dfrac{9}{25}=\dfrac{25-9}{25}$

$\cos^{2}x=\dfrac{16}{25}$

$\cos x=\pm\sqrt{\dfrac{16}{25}}$

$\cos\;x=\pm{\dfrac{4}{5}$

Como $90^{\circ}<x<180^{\circ}$, o cosseno é negativo, então:

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