Question

Resolver a equação 2cos(x)= 1

Answer 1

sen²x + cos²x = 1
cos²x = 1 - sen²x

2(1-sen²x) - sen x - 1 = 0
2 - 2sen²x - sen x - 1 = 0
-2sen²x - sen x + 1 = 0
2sen²x + sen x - 1 = 0

sen x = y
2y² + y - 1 = 0
∆ = b² - 4.a.c
∆ = 1² - 4.2.(-1)
∆ = 1 + 8
∆ = 9

y = (-b±√∆) / 2.a
y = (-1 ±√9) / 2.2
y = (-1 ± 3) / 4
y' = (-1 + 3)/4
y' = 2/4 = 1/2

y" = (-1-3) / 4
y" = -4/4 = -1

sen x = y
Para y = 1/2
sen x = 1/2
x = π/6 , 5π/6.

Para y = -1
sen x = -1
x = 3π/2