SOBRE ÁNGULOS EN TRIGONOMETRÍA

      347 comentarios en SOBRE ÁNGULOS EN TRIGONOMETRÍA

Uno de los primeros temas que abordan los docentes de Trigonometría, al trabajar con sus estudiantes de educación básica, es la Historia de dicha rama de las Matemáticas. Es común que se mencione, en dichas consultas, la cultura babilónica, con su sistema de medida sexagesimal y que se referencie también el sistema de radianesradianes. Teniendo en cuenta que las magnitudes son directamente proporcionales, al hacer conversiones de ángulos se emplea una regla de tres simple directa. Gráficamente se tiene la siguiente correspondencia en las áreas grises: Se muestran, a continuación unos ejemplos de conversiones de ángulos.

Ejemplos
Convertir 30° a radianes.
Empleando una regla de tres simple, se tiene:
180° π
30° x
De donde se llega a:
x=(30°∙π)/(180°)=(15°∙π)/(90°)=(5°∙π)/(30°)=(1∙π)/6=π/6

Las unidades de grados se cancelan entre sí. Por tanto: 30° = π/6
Convertir 5π/6 a radianes.
π 180°
5π/6 x
De forma análoga a la anterior:
x=(5π/6∙180°)/π=((900°∙π)/6)/(π/1)=(900°∙π)/6π=(900°)/6=150°
Es decir que, 5π/6 = 150°

Una forma mnemotécnica para recordar el proceso de conversión se aprecia en la siguiente ilustración: Grados sexagesimales Radianes

Escritor:  César A. Ruiz C.

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