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Home » Since \( t > 0 \), we take the positive root: - Red Crowns

Since \( t > 0 \), we take the positive root: - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 5Pregunta: Encuentra todos los ángulos $z \in [0^\circ, 360^\circ]$ que satisfacen la ecuación $\sin(2z) = \cos(z)$.

📌 Solución: Para resolver la ecuación $\sin(2z) = \cos(z)$, comenzamos utilizando la identidad del ángulo doble para seno, que establece que $\sin(2z) = 2\sin(z)\cos(z)$. Así, la ecuación se convierte en:

📌 Podemos factorizar $\cos(z)$:

📌 \cos(z)(2\sin(z) - 1) = 0.

📌 Esto nos da dos casos para resolver:

📌 $\cos(z) = 0$

📌 $2\sin(z) - 1 = 0 \implies \sin(z) = \frac{1}{2}$

📌 Caso 1: $\cos(z) = 0$

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