Question

1-) Dado Cos a = - 1/2 e π/2 < a < π

Answer 1

cos a = -1/2
pi/2 < a < pi
sen²a + cos²a = 1
sen²a + (-1/2)² = 1
sen²a + 1/4 = 1
sen²a = 1 - 1/4
sen²a = 3/4
sen a = \/(3/4)
sen a = \/3 / 2

a) sen 2a = 2.sena.cosa = 2 . \/3/2 . (-1/2) = (2.\/3.(-1)) /(1.2.2) = -2\/3/4 =   -\/3/2 --> = \/3/2 (2º quadrante)

b) cos 2a = cos²a - sen²a = (-1/2)² - (\/3/2)² = 1/4 - 3/4 = -2/4 = -1/2