Question

sabendo que sen a =3/5 e que 0< a < pi/2, calcule o cos (pi/3+a).

Answer 1

sen²a + cos²a = 1

cos²a = 1 - sen²a

cos²a = 1 - (3/5)²

cos²a = 1 - 9/25

cos²a = 25/25 - 9/25 = 16/25

cosa = √16/√25 = 4/5

cos π/3 = cos 60 = 1/2

sen π/3 = sen 60 = √3/2

cos(a+b) = cosacosb - senasenb

cos(π/3 + a) = cosπ/3*cosa - senπ/3*sena

cos(π/3 + a) = (1/2)*(4/5) - (√3/2)*(3/5)

cos(π/3 + a) = 4/10 - (3√3)/10 = (4-3√3)/10 = 1/10*(4 - 3√3)