Question

Resuelve e indica la primera y segunda solución de la ecuación trigonométrica:
Cos5x = 1/2​

Answer 1

Respuesta:

S = { -π/15, π/3, 7π/15}

Explicación paso a paso:

cos5x = 1/2

cos5x = cosπ/3

5x = ±π/3 + 2kπ, k ∈ Z

x = ±π/15 + 2kπ/5

P/k = 0 ⇒ x = ±π/15 = -π/15 o π/15 (1ª solução)

P/k = 1 ⇒ x = ±π/15 + 2π/5

x = -π/15 + 2π/5 = (-π+6π)/15 = 5π/15 = π/3

o

x = π/15 + 2π/5 = 3π/15 = (π + 6π)15 = 7π/15

2ª solução: π/3 o 7π/15