Question

Sen2a=4-9,a€[0,2]obtenha o valor de cos a

Answer 1

Bom dia

sen(2a) = 4/9,a € [0,2π] obtenha o valor de cos(a)

sen(2a) = 2sen(a)*cos(a) = 4/9 
sen(a)*cos(a) = 2/9 
sen(a) = 2/(9cos(a))

sen²(a) + cos²(a) = 1
4/(81cos²(a) + cos²(a) = 1
4/81 + cos⁴(a) = cos²(a) 

y = cos²(a)

y² - y + 4/81 = 0 
81y² - 81y + 4 = 0

delta
d² = 81² - 16*81
d² = 5265 
d = 9√65

y1 = (81 + 9√65)/162 = 0.94790
y2 = (81 + 9√65)/162 = 0.05210
y = cos²(a)

cos²(a) = 0.94790
cos²(a) = 0.05210

cos(a) = -√0.94790 = -0.973602cos(a) = √0.94790  =  0.973602cos(a) = -√0.05210 = -0.228254
cos(a) = √0.05210  = n0.228254