Introduccion

[img]https://i.pinimg.com/736x/43/8b/75/438b757d8cb6fec3647e9dff31b1fdc9.jpg[/img][br]La enseñanza y el aprendizaje de la trigonometría han evolucionado más allá de la memorización de fórmulas y la resolución estática de triángulos en el papel. En el contexto de la educación matemática contemporánea, la visualización dinámica juega un papel crucial para que los estudiantes logren una comprensión conceptual profunda. El uso de Tecnologías de la Información y la Comunicación (TIC), y específicamente de software de geometría dinámica como GeoGebra, permite transformar conceptos abstractos en representaciones visuales e interactivas tangibles.[br][br]El presente trabajo tiene como objetivo resolver una serie de problemas trigonométricos seleccionados, utilizando a GeoGebra no solo como una herramienta de cálculo, sino como un medio pedagógico fundamental. A través del diseño de un libro digital estructurado y el desarrollo de [i]applets[/i] interactivos, se busca conectar la rigurosidad del lenguaje algebraico con la intuición geométrica. Cada actividad aquí presentada sigue un proceso metodológico riguroso: desde el análisis y la modelación matemática del problema, pasando por la verificación analítica paso a paso, hasta la creación de escenarios dinámicos donde variables como ángulos y distancias pueden ser exploradas libremente.[br][br]Con este enfoque, se pretende demostrar cómo la tecnología potencia la competencia de resolución de problemas y fundamenta una práctica docente orientada al aprendizaje significativo y la rigurosidad científica.[br]

Ejercicio 1

1. Calcula las seis funciones trigonométricas para cada uno de los siguientes triángulos rectángulos.[br][img]data:image/png;base64,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[/img][br][*][b]Datos dados:[/b] Cateto a (vertical, lado BC) = 13[br][list][*]Hipotenusa c (lado AB) = 17[br][/*][*]Ángulo C = 90°[br][/*][/list][/*][*][b]1. Hallar el lado faltante (Cateto b o lado AC):[/b][br][/*][*][b][math]b=\sqrt{c^2-a^2}=\sqrt{17^2-13^2}=\sqrt{289-169}=\sqrt{120}=10.95[/math][br][/b][/*][*][b][b]2. Hallar los ángulos faltantes (A y B):[/b][br][list][*]Para el ángulo A: Usamos el seno, ya que conocemos su cateto opuesto (13) y la hipotenusa (17).[br][/*][/list][math]sen\binom{A}{ }=\frac{13}{17}=0.7647\Longrightarrow A=sen^{-1}\binom{0.7647}{ }=49.88°[/math][br]Para el ángulo B: Como los ángulos agudos deben sumar 90°[/b][/*][*][b][math]B=90°-49.88°=40.12°[/math][br][br][/b][/*]

Referencias Bibliográficas

Cuéllar Carvajal, J. A. (2019). Geometría y trigonometría: Conceptos y aplicaciones (4.ª ed.). McGraw-Hill.[br][br]Swokowski, E. W., & Cole, J. A. (2011). Álgebra y trigonometría con geometría analítica (13.ª ed.). Cengage Learning.[br][br]Sullivan, M. (2013). Álgebra y trigonometría (9.ª ed.). Pearson.[br][br]Carpinteyro Vigil, E. (2018). Geometría y trigonometría: conceptos y aplicaciones: ( ed.). Ciudad de México, Mexico: Grupo Editorial Patria. Recuperado de https://elibro.net/es/ereader/bibliotecautpl/40528?page=10.

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