Question

dado o cos x = 4/7, determine sen x e a tg x

Answer 1

sen²x+cos²x=1 ⇒ sen²x+(4/7)²=1 ⇒ sen²x=1-16/49=(49-16)/49=33/49 ⇒ senx=√33/49 ⇒ senx=√33/7

tgx=senx/cosx=(√33/7)/(4/7)=(√33/7)*(7/4)=6/4=√33/4

Answer 2

Da relação fundamental:
sen²x + cos²x = 1
sen²x + (4/7)² = 1
sen²x + 16/49 = 1
sen²x = 1 - $\frac{16}{49}$
sen²x = $\frac{33}{49}$
senx = $\sqrt{ \frac{33}{49} }$
senx = $\frac{ \sqrt{33} }{7}$

Tgx = senx/cosx
tgx = $\frac{ \frac{ \sqrt{33} }{7} }{ \frac{4}{7} }$
tgx = $\frac{ \sqrt{33} }{7} * \frac{7}{4}$
tgx = $\frac{7 \sqrt{33} }{28}$
tgx = $\frac{ \sqrt{33} }{4}$