Question

sendo 0<x<pi/2 e cos x=2 raiz de 2/3, calcule sen x​

Answer 1

Resposta:

sen x = 2/3

sen²x + cos²x = 1

(2/3)² + cos²x = 1

cos²x = 1 - 4/9

cos²x = 5/9

cos x = √5/3

(A)

sen 2x = 2*senx*cosx = 2*(2/3)*(√5/3) = 4√5/9

sen 2x = 4√5/9

(B)

cos 2x = cos²x - sen²x = (√5/3)² - (2/3)² = 5/9 - 4/9 = 1/9

cos 2x = 1/9

Espero ter ajudado     : D