Question

determine cos x
$\: \sin \: x = - \frac{2}{5} \: com \: 3 \frac{\pi}{2} < x \: 2\ \: pi \:$
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Answer 1

$\large\boxed{\begin{array}{l}\sf se\,x\in\bigg[\dfrac{3\pi}{2},2\pi\bigg]~cos(x)>0.\\\sf sen(x)=-\dfrac{2}{5}\implies sen^2(x)=\dfrac{4}{25}\\\\\sf cos^2(x)=\dfrac{25}{25}-\dfrac{4}{25}=\dfrac{21}{25}\\\\\sf cos(x)=\dfrac{\sqrt{21}}{\sqrt{25}}=\dfrac{\sqrt{21}}{5}\end{array}}$