Question

sabendo que tg a = 1/4, calcule sen 2a

Answer 1

Vamos lá:

tg a = 1/4
tg a = sen a/cos a

sen^2 a + cos^2 a = 1
tg^2 a + 1 = 1/cos^2 a
(1/4)^2 + 1 = 1/cos^2 a
1/cos^2 a = 1/8 + 1
1/cos^2 a = 1/8 + 8/8
1/cos^2 a = 9/8
9.cos^2 a = 8
cos^2 a = 8/9
cos a = (2V2)/3

tg a = 1/4
tg a = sen a/cos a
sen a/(2V2/3) = 1/4
sen a.3/(2V2) = 1/4
sen a = (1/4)/[3/(2V2)]
sen a = (1/4).(2V2)/3
sen a = (2V2)/12
sen a = V2/6

sen (2a) = 2.sen a.cos a
sen (2a) = 2.(V2/6).(2V2)/3
sen (2a) = 16/18
sen (2a) = 8/9

Espero ter ajudado