Question

sabendo que sec x= 5/2 e 3pi/2<x>2pi obtenha as demais razoes trigonometricas de x 

Answer 1

Considerando que o arco é do terceiro quadrante:

$\boxed{cos(x)=\frac{1}{sec(x)}=\frac{2}{5}}\\ \\ \boxed{sen(x)=\sqrt{1-cos^2(x)}=\sqrt{1-\frac{4}{25}}=\sqrt{\frac{21}{25}}=-\frac{\sqrt{21}}{5}}\\ \\ \boxed{cossec(x)=\frac{1}{sen(x)}=-\frac{5}{\sqrt{21}}=-\frac{5\sqrt{21}}{21}}\\ \\ \boxed{tan(x)=\frac{sen(x)}{cos(x)}=\frac{-\frac{\sqrt{21}}{5}}{\frac{2}{5}}=-\frac{\sqrt{21}}{2}}\\ \\ \boxed{cotg(x)=\frac{1}{tan(x)}=-\frac{2}{\sqrt{21}}=-\frac{2\sqrt{21}}{21}}$