Resposta:
tg a = -√0,96 / 0,2 = - 4,89
Explicação passo a passo:
3π/2 < a < 2π
cos a = 0,2
tg a = ?
sen a / cos a
sen² a = 1 - cos² a
sen² a = 1 - 0,2²
sen² a = 1 - 0,04
sen² a = 0,96
sen a = -√0,96
tg a = -√0,96 / 0,2 = - 4,89
[tex]\large\boxed{\begin{array}{l}\rm\dfrac{3\pi}{2}<a<2\pi\longrightarrow \underline{a}\,pertence\,ao\,4^o\,quadrante\\\rm cos(a)=0,2=\dfrac{1}{5}\\\\\rm sec(a)=5\longrightarrow sec^2(a)=25\\\\\rm tg^2(a)=sec^2(a)-1\\\rm tg^2(a)=25-1\\\rm tg^2(a)=24\\\rm no\,4^o\,quadrante\,tg(a)\,\acute e\,negativo.\\\rm tg(a)=-\sqrt{24}\\\rm tg(a)=-\sqrt{4}\cdot\sqrt{6}\\\rm admite\,\sqrt{6}=2,449\end{array}}[/tex]
[tex]\large\boxed{\begin{array}{l}\rm tg(a)=-2\cdot2,449\\\rm tg(a)=-4,898\end{array}}[/tex]
