Graham Moran
12/19/2023 · Middle School
Ecuaciones trigonométricas. Dada la siguiente ccuación trigonométrica: 1) presente el paso a paso para determinar su solución. 2) Utilice el software libre educativo GeoGebra para graficar la ectuación trigonométrica y para verificar que la solución del literal i) encontrada analiticamente es correcta. D. \( \mathbf{2 s e n 2}(\boldsymbol{\theta})-\mathbf{3 s e n}(\boldsymbol{\theta})+\mathbf{1}=\mathbf{0} \)
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Para resolver la ecuación \( 2 \sen^2(\theta) - 3 \sen(\theta) + 1 = 0 \), sustituye \( x = \sen(\theta) \) y resuelve la ecuación cuadrática \( 2x^2 - 3x + 1 = 0 \). Las soluciones son \( \sen(\theta) = 1 \) y \( \sen(\theta) = \frac{1}{2} \), lo que da \( \theta = \frac{\pi}{2} + 2k\pi \), \( \theta = \frac{\pi}{6} + 2k\pi \), y \( \theta = \frac{5\pi}{6} + 2k\pi \). Verifica las soluciones con GeoGebra.
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