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Introducción a Gráficas; El Círculo Unitario; Funciones Seno y Coseno; Características y Simetría; Transformaciones (A y B)

Gráficas de Funciones Trigonométricas

Matemáticas

Gráficas de Funciones Trigonométricas

Explorando las representaciones visuales de seno y coseno.

Agenda

• Introducción a Gráficas

• El Círculo Unitario

• Funciones Seno y Coseno

• Características y Simetría

• Transformaciones (A y B)

Introducción a Gráficas Trigonométricas

Exploraremos cómo las funciones seno y coseno, fundamentales en matemáticas, se representan visualmente a través de sus gráficas. Estas gráficas nos permiten entender patrones repetitivos en fenómenos como las ondas de sonido y la luz.

Gráfica de la identidad trigonométrica y = sin²(x) + cos²(x) = 1

Importancia de las Gráficas Trigonométricas

Modelan fenómenos cíclicos como mareas, ondas de sonido y electricidad. Son cruciales para entender el mundo.

El Círculo Unitario: La Base

El círculo unitario tiene un radio de 1. Los puntos en su circunferencia definen los valores de seno y coseno. Es clave para entender las funciones trigonométricas.

Gráfica de la función seno (y = sin(x)) con rango -1 a 1

Función Seno: Definición

• Coordenada 'y' en círculo unitario.

• Valor de seno para ángulos.

• Dominio: todos los números reales.

• Rango: entre -1 y 1.

Gráfica de la función coseno y = cos(x) en el círculo unitario

Función Coseno: Definición

• Relaciona el ángulo con la coordenada "x".

• En el círculo unitario, es la "x".

• Empieza en 1, disminuye a -1, regresa.

• Su dominio son todos los números reales.

Periodicidad y Simetría

Las funciones seno y coseno son periódicas, repitiendo sus valores cada 2π radianes. Ambas muestran simetría: el seno es impar, el coseno es par. Estas propiedades son clave para entender sus gráficas.

Dibujando y = sen(x)

Construimos la gráfica básica de y = sen(x) identificando puntos clave como máximos, mínimos y ceros en el círculo unitario.

Gráfica de y = sen(x/2) con máximos y mínimos marcados

Gráficas de Funciones Trigonométricas

Introducción a Gráficas; El Círculo Unitario; Funciones Seno y Coseno; Características y Simetría; Transformaciones (A y B)

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