Question

Ache tg x, sabendo que cossec x = 3, com 0 < X < $\frac{ \pi}{2}$.

Answer 1

Vamos lá.

cossec x = 3

$\frac{1}{senx}$ = 3

3senx = 1

senx = $\frac{1}{3}$

sen²x+cos²x = 1

($\frac{1}{3}$)²+cos²x = 1

cos²x = 1 - $\frac{1}{9}$

cos²x = $\frac{8}{9}$

cosx = √($\frac{8}{9}$)

cosx = $\frac{ \sqrt{8} }{3}$

cosx = $\frac{ \sqrt{ 2^{2}*2 } }{3}$

cosx = $\frac{2 \sqrt{2} }{3}$


tgx = $\frac{sen x}{cosx}$

tgx = $\frac{1}{ \frac{2}{ \frac{2 \sqrt{2} }{3} } }$

tgx = $\frac{1}{3} *\frac{3}{2 \sqrt{2} }$

tgx = $\frac{3}{6 \sqrt{2} }$

tgx = $\frac{1}{2 \sqrt{2} }$

tgx = $\frac{1* \sqrt{2} }{2 \sqrt{2}* \sqrt{2} }$

tgx = $\frac{ \sqrt{2} }{2 \sqrt{4} }$

tgx = $\frac{ \sqrt{2} }{2*2}$

tgx = $\frac{ \sqrt{2} }{4}$

Espero ter lhe ajudado. Abraços