Question

Dado sen a=2/3,com 0<a<pi/2 determine sen 2a, cos 2a e tg 2a

Answer 1

sen²a + cos²a = 1 => (2/3)² + cos²a = 1 => cos²a = 1 - 4/9 => cos²a = 5/9
cosa = √5/3
sen2a = 2sena cosa
sen2a + 2.2/3.√5/3
sen2a = 4√5/9

cos2a = 1 - 2sen²a
cos2a = 1 - 2. (2/3)²
cos2a = 1 - 2.4/9
cos2a = (9 - 8)/9
cos2a = 1/9

tg2a = 2tga/(1 - tg²a)
tga = sena/cosa
tga = 2/3 :√5/3
tga  = 2/3 . 3/√5
tga = 2/√5
tga = 2√5/5

tg2a = 2.2√5/5 :(1 - 4.5/25)
tg2a = 4√5/5 : (25 - 20)/25
tg2a = 4√5/5 . 25/5
tg2a = 20√5/5