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    determina en que cuadrante son positivas sólo las funciones trigonométricas secante y coseno.

    Santiago

    Chicos, ¿alguien sabe la respuesta?

    obtenga determina en que cuadrante son positivas sólo las funciones trigonométricas secante y coseno. de este sitio.

    El Círculo Unidad en Trigonometría

    El Círculo Unidad en Trigonometría

    Objetivos de Aprendizaje

    ·         Entender el círculo unidad, ángulo de referencia, lado terminal, posición estándar.

    ·         Encontrar los valores exactos de la función trigonométrica para ángulos que miden 30°, 45°, y 60° usando el círculo unidad.

    ·         Encontrar los valores exactos de la función trigonométrica para cualquier ángulo cuyo ángulo de referencia mida 30°, 45°, o 60°.

    ·         Determinar los cuadrantes donde el seno, coseno, y tangente son positivos y negativos.

    Introducción

    Los matemáticos crean definiciones porque tienen una utilidad para resolver ciertos tipos de problemas. Por ejemplo, las seis funciones trigonométricas se definieron originalmente en términos de triángulos rectángulos porque eran útiles para resolver problemas del mundo real que involucran triángulos rectángulos, como por ejemplo encontrar ángulos de elevación. El dominio, o conjunto de valores de entrada, de estas funciones es el conjunto de ángulos entre 0° y 90°. Ahora aprenderás nuevas definiciones para estas funciones en las que el dominio es el conjunto de todos los ángulos. Las nuevas funciones tendrán los mismos valores que las funciones originales cuando la entrada sea un ángulo agudo. En un triángulo rectángulo sólo puedes tener ángulos agudos, pero verás que la definición se extiende para incluir otros ángulos.

    Un uso de estas nuevas funciones es que pueden ser utilizadas para encontrar los lados y medidas de ángulos desconocidos en cualquier triángulo. Estas nuevas funciones pueden usarse en muchas situaciones que no tienen nada que ver con triángulos.

    Antes de ver las nuevas definiciones, necesitas familiarizarte con la manera estándar que usan los matemáticos para dibujar y nombrar ángulos.

    Ángulos Generales

    En geometría, sabes que un ángulo está formado por dos rayos. Los rayos se unen en un punto llamado vértice.

    En trigonometría, los ángulos se posicionan en ejes de coordenadas. El vértice siempre se coloca en el origen y uno de los rayos siempre se coloca en el eje- positivo. Este rayo se llama lado inicial del ángulo. El otro rayo se llama lado terminal del ángulo. A este posicionamiento del ángulo se llama posición estándar. La letra Griega teta () se usa normalmente para representar una medida de un ángulo. A continuación se muestran dos ángulos en la posición estándar.

    Cuando se dibuja un ángulo en la posición estándar, no tiene dirección. En el dibujo anterior, observa que hay flechas curvas pequeñas. La de la izquierda va en contra de las manecillas del reloj y se define como un ángulo positivo. La de la derecha va a favor de las manecillas del reloj y se define como un ángulo negativo. Si usas un transportador para medir los ángulos, tendrás que miden 50° en ambos casos. Nos referimos al primero como un ángulo de 50°, y al secundo como un ángulo de .

    ¿Por qué es necesario tener ángulos negativos? Al igual que todas las definiciones, es una cuestión de conveniencia. Una nave espacial en una órbita circular alrededor del ecuador de la Tierra podría estar viajando en cualquiera de las dos direcciones. Entonces podrías decir que viaja en un ángulo de  para indicar que va en la dirección opuesta que otra nave que viaja en un ángulo de 50°. ¿Por qué ir en contra de las manecillas del reloj es positivo? Es simplemente una convención — algo en lo que los matemáticos se han puesto de acuerdo — porque una dirección debe ser positiva y la otra debe ser negativa.

    Par ver cómo ángulos positivos resultan de una rotación en contra de las manecillas del reloj, y ángulos negativos de una rotación a favor de las manecillas del reloj, intenta con el ejercicio interactivo siguiente. Ya sea que introduzcas una medida de un ángulo en el campo llamado “Ángulo” y presionas enter o usas el control deslizante para mover el lado terminal de ángulo pasando por los cuadrantes.

    This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

    Ejemplo

    Problema

    Dibujar un ángulo de 160° en la posición estándar.

    El ángulo es positivo, por lo que empiezas en el eje- y vas hasta 160° a favor de las manecillas del reloj.

    Ejemplo

    Problema

    Dibujar un ángulo de en la posición estándar.

    El ángulo es negativo, por lo que empiezas en el eje-y vas hasta 200° en contra de las manecillas del reloj. Recuerda que 180° es una línea recta. Eso significa que llegarás al eje negativo, y lo pasarás otros 20°.

    Observa que los lados terminales en los dos ejemplos anteriores son el mismo, pero representan ángulos distintos. A esos pares de ángulos se les llama ángulos coterminales.

    fuente : www.montereyinstitute.org

    Signos de las funciones trigonométricas

    Los signos de las funciones trigonométricas varían dependiendo del cuadrante en el que se encuentren, aquí te mostraré que signo tiene cada una en cada..

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    HomeÁlgebraFuncionesSignos de las funciones trigonométricas

    Álgebra, Funciones, Trigonometría

    Signos de las funciones trigonométricas

    Monica Casillas Brizuela 8 Años Ago

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    Los signos de las funciones trigonométricas varían dependiendo del cuadrante en el que se encuentren, aquí te mostraré que signo tiene cada una en cada cuadrante.

    Signos de las funciones trigonométricas

    sen α = c.opuesto/hipotenusa

    cos α = c.adyacente/hipotenusa

    tang α = c.opuesto/ c.adyacente

    Primer cuadrante

    En este cuadrante el cateto adyacente está sobre el eje “x” y el cateto opuesto sobre el eje “y”, la hipotenusa es el radio de la circunferencia.

    Como el c, opuesto, c. adyacente y la hipotenusa son positivos, todas las funciones trigonométricas son positivas en el primer cuadrante.

    Segundo cuadrante

    En este cuadrante, el cateto adyacente es negativo y el cateto opuesto es positivo también es positiva la hipotenusa. Por lo que el coseno, la tangente, la secante y la cotangente son negativas.

    Tercer cuadrante

    En este cuadrante el cateto adyacente y el cateto opuesto son negativos y la hipotenusa es positiva. Por lo tanto la tangente y la cotangente resultan positivas y las demás negativas.

    Cuarto cuadrante

    En este cuadrante el cateto adyacente es positivo y el cateto opuesto es negativo y la hipotenusa es positiva. Por lo tanto solo el coseno y la secante serán positivas.

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    Determina en que cuadrante son positivas sólo las funciones trigonométricas secante y coseno.a.

    Determina en que cuadrante son positivas sólo las funciones trigonométricas secante y coseno.a. Tercer cuadran… Recibe ahora mismo las respuestas que necesitas!

    Determina en que cuadrante son positivas sólo las funciones trigonométricas secante y coseno.a. - Brainly.lat

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    fuente : brainly.lat

    ¿Quieres ver la respuesta o más?
    Santiago 6 month ago
    4

    Chicos, ¿alguien sabe la respuesta?

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