Question

Quais são os valores possíveis do quociente sen x/cos x sabendo que sen x =0,5???​
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Answer 1

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$\sf sen(x)=0,5=\dfrac{1}{2}\implies x=\dfrac{\pi}{6}~ou~x=\dfrac{5\pi}{6}\\\sf se ~x=\dfrac{\pi}{6}:\\\sf sen(x)=\dfrac{1}{2}~e~cos(x)=\dfrac{\sqrt{3}}{2}\\\sf \dfrac{sen(x)}{cos(x)}=\dfrac{\frac{1}{\diagdown\!\!\!2}}{\frac{\sqrt{3}}{\diagdown\!\!\!2}}=\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{3}}{3}$

$\sf se~x=\dfrac{5\pi}{6}:\\\sf sen(x)=\dfrac{1}{2}~e~cos(x)=-\dfrac{\sqrt{3}}{2}\\\sf\dfrac{sen(x)}{cos(x)}=-\dfrac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=-\dfrac{1}{\sqrt{3}}=-\dfrac{\sqrt{3}}{3}\\\rm portanto:\\\Large\sf \dfrac{sen(x)}{cos(x)}=\begin{cases}\sf\dfrac{\sqrt{3}}{3}~,se~x=\dfrac{\pi}{6}\\\sf-\dfrac{\sqrt{3}}{3}~,se~x=\dfrac{5\pi}{6}\end{cases}~\blue{\checkmark}$