Ecuación trigonométrica para el intervalo indicado: 2cosx - √2 = 0, x ∈ [0, 2π)
Resolvemos paso a paso una ecuación trigonométrica sencilla con coseno:2cosx − √2 = 0 con la condición x ∈ [0, 2π), es decir, buscamos todas las soluciones dentro de una vuelta completa.
Veremos cómo despejar el coseno, cómo reconocer el valor notable cosx = √2/2 y cómo localizar las soluciones correctas dentro del intervalo [0, 2π).
La clave está en recordar que el coseno es positivo en el primer y cuarto cuadrante. Por eso las soluciones serán: x = π/4 y x = 7π/4
Una clase breve, clara y directa para entender cómo resolver ecuaciones trigonométricas básicas usando la circunferencia trigonométrica y los ángulos notables.
📌 Contenido del vídeo:
00:01 Presentación de la ecuación
1:43 Reconocimiento de los ángulos notables
3:12 Despejamos el coseno
00:50 Solución en el 1er cuadrante
01:20 Solución en el 4o cuadrante
02:00 Conclusión
✅ Solución:
x = π/4, 7π/4
#matematicas #trigonometria #ecuacionestrigonometricas #coseno #matematicasconjuan
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