Question

Sabendo que tg x = 3, 0 < x < pi/2, obter senx e cosx.

Answer 1

tgx = 3
senx/cosx = 3
senx = 3cosx
sen²x = 9cos²x
sen²x - 9cos²x = 0
sen²x - 9cos²x + 9.(sen²x+cos²x) = 9.1

10sen²x -9cos²x+9cos²x=9
10sen²x = 9
sen²x = 9/10
senx = 3/√10 = 3√10/10

cosx = senx/3
cosx = 3/3√10=
1/√10=√10/10

espero ter ajudado, abs