Question

Sabendo que  pi/2 < X < pi e cossec x = 4, obtenha tg x, cotg x e sec x 

Resposta: Tg x =  √ /

Cotg x =  √

Sec x =   √ /

Answer 1

$<var>sen x=\frac{1}{cossec x}=\frac{1}{4}</var>$

 

 

$<var>cos x=\sqrt{1-sen^2 x}=\sqrt{1-(\frac{1}{4})^2}=\sqrt{\frac{15}{16}}=\frac{\sqrt{15}}{4}</var>$ 

 

 

$<var>tan x=\frac{sen x}{cos x}=\frac{\frac{1}{4}}{\frac{\sqrt{15}}{4}}=\frac{1}{\sqrt{15}}=\frac{\sqrt{15}}{15}</var>$ 

 

 

$<var>cotg x=\frac{1}{tan x}=\frac{15}{\sqrt{15}}=\sqrt{15}</var>$ 

 

$<var>sec x=\frac{1}{cos x}=\frac{1}{\frac{\sqrt{15}}{15}}=\sqrt{15}</var>$