Question

5 317 3. Se sent = 0 [m, ), então o valor de eo e TL o 13 4 tg(20) é: a) 12 13 120 b) - 119 120 C 119 d) 1 V3 e) whal​

Answer 1

$\large\boxed{\begin{array}{l}\rm sen(\theta)=\dfrac{5}{13}\longrightarrow sen^2(\theta)=\dfrac{25}{169}\\\\\rm cos^2(\theta)=\dfrac{169}{169}-\dfrac{25}{169}=\dfrac{144}{169}\\\\\rm cos(\theta)=-\sqrt{\dfrac{144}{169}}=-\dfrac{12}{13}\\\\\rm tg(\theta)=\dfrac{\frac{5}{\diagup\!\!\!\!\!\!13}}{-\frac{12}{\diagup\!\!\!\!\!13}}=-\dfrac{5}{12}\\\\\rm tg(2\theta)=\dfrac{2tg(\theta)}{1-tg^2(\theta)}\\\\\rm tg(2\theta)=\dfrac{2\cdot-\frac{5}{12}}{1-\bigg(-\dfrac{5}{12}\bigg)^2}\end{array}}$

$\large\boxed{\begin{array}{l}\rm tg(2\theta)=\dfrac{-\frac{5}{6}}{1-\frac{25}{144}}\\\\\rm tg(2\theta)=\dfrac{-\frac{5}{6}}{\frac{119}{144}}\\\\\rm tg(2\theta)=-\dfrac{5}{\backslash\!\!\!6}\cdot\dfrac{\diagup\!\!\!\!\!\!144^{24}}{119}\\\\\rm tg(2\theta)=-\dfrac{120}{119}\\\\\huge\boxed{\boxed{\boxed{\boxed{\rm\dagger\red{\maltese}~\blue{alternativa~b}}}}}\end{array}}$