againjack againjack

24-04-2022
Mathematics

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Solve the equation on the interval [0,2π).

8cos^2x+4cosx=0

Select all correct solutions.
0
π/3
π/2
2π/3
π
4π/3
5π/3
3π/2
11π/6

Respuesta :

Аноним Аноним

24-04-2022

Answer:

π/2, 2π/3, 3π/2, 4π/3.

Step-by-step explanation:

8cos^2x+4cosx=0

4cosx(2cosx + 1) = 0

so cosx = 0, -1/2.

Therfore

When cos x = 0:

x = π/2, 3π/2

When cos x = -1/2:

x = 2π/3, 4π/3.

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