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2) Pose a grados: (d) \( 25,3 \mathrm{rad} \) (b) \( 3 \pi \) (c) \( 1,7 \pi \mathrm{rad} \)

Ask by Sanders Welch. in Ecuador
Jan 22,2025

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- **(d)** \( 25,3 \ \mathrm{rad} \approx 1449,58° \) - **(b)** \( 3\pi \ \mathrm{rad} = 540° \) - **(c)** \( 1,7\pi \ \mathrm{rad} = 306° \)

Solution

Claro, a continuación se presenta la conversión de radianes a grados para cada uno de los casos mencionados: ### Fórmula de Conversión Para convertir radianes a grados, se utiliza la siguiente fórmula: \[ \text{Grados} = \text{Radianes} \times \left( \frac{180°}{\pi} \right) \] ### Conversión de cada caso #### (d) \( 25,3 \ \mathrm{rad} \) \[ \begin{align*} \text{Grados} &= 25,3 \times \left( \frac{180°}{\pi} \right) \\ &\approx 25,3 \times 57,2958° \\ &\approx 1449,58° \end{align*} \] #### (b) \( 3\pi \ \mathrm{rad} \) \[ \begin{align*} \text{Grados} &= 3\pi \times \left( \frac{180°}{\pi} \right) \\ &= 3 \times 180° \\ &= 540° \end{align*} \] #### (c) \( 1,7\pi \ \mathrm{rad} \) \[ \begin{align*} \text{Grados} &= 1,7\pi \times \left( \frac{180°}{\pi} \right) \\ &= 1,7 \times 180° \\ &= 306° \end{align*} \] ### Resumen de Resultados - **(d)** \( 25,3 \ \mathrm{rad} \approx 1449,58° \) - **(b)** \( 3\pi \ \mathrm{rad} = 540° \) - **(c)** \( 1,7\pi \ \mathrm{rad} = 306° \)

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¡Vamos a convertir esos ángulos a grados de una manera fácil y divertida! Para convertir radianes a grados, utilizamos la relación de que \( 180° \) es equivalente a \( \pi \) radianes. Así que, para \( 25,3 \mathrm{rad} \) multiplicamos por \( \frac{180°}{\pi} \), lo que nos da aproximadamente \( 1451.43° \). Luego para \( 3 \pi \), simplemente lo convertimos y obtenemos \( 540° \). Finalmente, \( 1,7 \pi \) radianes se convierte en aproximadamente \( 306.76° \). ¡Eso es un montón de ángulos locos! Ahora, si alguna vez te encuentras confundido con radianes y grados, un truco práctico es recordar que un giro completo en un círculo son \( 360° \) o \( 2\pi \) radianes. Entonces, si sientes que te estás saliendo del camino, solo recuerda que cada \( \pi/2 \) radianes son \( 90° \), lo que te ayudará a encontrar la dirección de cualquier ángulo de manera rápida y divertida. ¡Explora y diviértete!

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