If sinx= $\frac{2}{3}$, then find the value of cos 3x.

0.6735 -0.8765 -0.5797 0.5678

-0.5797

sinx =  \(\frac{2 }{3}\) sin²x + cos²x = 1 cos²x = 1 -  \(\frac{4 }{9}\) = \(\frac{5 }{9}\) cosx = \(\frac{√5 }{3}\) We know, cos3x = 4cos³x - 3cosx = 4 × ( \(\frac{√5 }{3}\) )³ - 3 × \(\frac{√5 }{3}\) = \(\frac{20√5 }{27}\) - √5 = - \(\frac{7√5 }{27}\) = - 0.5797