Question

Deter mine cos, sabendo que sen=3raizde13 sobre 13 e tg 3 sobre 2

Answer 1

Expressões dadas:

$\sin \alpha = \dfrac{3\sqrt{13}}{13}\\\\ \tan \alpha = \dfrac{3}{2}\\\\\\ Sabemos\ que:\\\\ \tan \alpha = \dfrac{\sin \alpha}{\cos \alpha}\\\\\\ Logo:\\\\ \cos \alpha = \dfrac{\sin \alpha}{\tan \alpha}\\\\\\ Resolvendo:\\\\ \cos \alpha = \dfrac{\frac{3\sqrt{13}}{13}}{\frac{3}{2}}\\\\ \cos \alpha = \dfrac{3\sqrt{13}}{13} \times \dfrac{2}{3}\\\\ \boxed{\cos \alpha = \dfrac{6\sqrt{13}}{39}}$


Espero ter ajudado.
Bons estudos!