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Circunferencia Unitaria: Guía Interactiva

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Circunferencia Unitaria: Guía Interactiva

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Guía interactiva de la circunferencia unitaria

Created by

Daniel Martinez
Daniel Martinez
Colombia

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Circunferencia Unitaria: Guía Interactiva
 

Circunferencia Unitaria: Guía InteractivaOnline version

Guía interactiva de la circunferencia unitaria

by Daniel Martinez
1

Introducción a la circunferencia unitaria

La circunferencia unitaria es el conjunto de puntos (x, y) en el plano con radio 1 centrados en el origen. Cada punto representa (cos θ, sin θ).

2

Qué es θ y por qué importa

El ángulo θ mide la rotación desde el eje positivo x. En la circunferencia unitaria, cos θ es x y sin θ es y de cada punto.

3

Ángulos y coordenadas básicas

Conoce ángulos comunes: 0, π/6, π/4, π/3, π/2. Sus coordenadas son (cos θ, sin θ). Practica convirtiendo entre grados y radianes.

4

Cuadrantes y signos

En cada cuadrante, las coordenadas cambian de signo. I (+,+), II (−,+), III (−,−), IV (+,−).

5

Mapa de valores especiales

Memoriza cos y sin para θ = 0, π/2, π, 3π/2. Esto acelera resolver pendientes y ángulos recíprocos.

6

Ejercicio interactivo 1

Determina las coordenadas de θ = π/3 y θ = 2π/3. Respuesta: (1/2, √3/2) y (−1/2, √3/2).

7

Ejercicio interactivo 2

Identifica el signo de x e y para cada θ: 30°, 150°, 210°, 330°. Explica razonando en cada caso.

8

Ángulos en grados y radianes

Conversión rápida: 180° = π rad. Practica convertir entre deg y rad con ejemplos: 45°, 60°, 120°, 300°.

9

Aplicaciones en problemas

Un punto en la circunferencia unitaria tiene θ = 135°. ¿Qué son x e y? x = −√2/2, y = √2/2.

10

Cierre y reflexión

Recuerda: cada punto representa una pareja (cos θ, sin θ). Utiliza esta relación para resolver problemas de ángulo y movimiento.
 
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