Razones trigonométricas

Para definir y representar las razones trigonométricas comenzamos dibujando la circunferencia goniométrica, para lo que utilizamos la herramienta [b]Circunferencia (centro-radio)[/b], dibujando la circunferencia que tiene centro en el origen de coordenadas y radio 1 unidad.[br]Para visualizar mejor las representaciones de las razones, aplicamos un zoom a la vista gráfica.[br][br][img 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continuación, situamos un punto cualquiera A en la circunferencia y marcamos el punto B(1, 0).[br]El punto A determinará junto con O y B un ángulo que irá variando al mover A por la circunferencia.[br]Obtenemos el ángulo utilizando la herramienta [b]Ángulo[/b] y dibujamos el segmento OA, tal y como aparece en la imagen siguiente:[br][br][img width=278,height=248]data:image/png;base64,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[/img][br]Trazamos a continuación la recta perpendicular al eje X por el punto A, determinando el punto de[br]intersección de esta recta con el eje X.[br][br][img 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[/img][br][br]Dibujamos el segmento AC y ocultamos la recta.[br][br][img 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trabajar con ángulos en la circunferencia goniométrica, sabemos que el seno del ángulo es la medida del[br]segmento AC que debemos crear con la herramienta [b]Segmento[/b], y el coseno del ángulo la medida del segmento OC ya que en el triángulo rectángulo AOC, la hipotenusa es igual a 1.[br]Por tanto, tenemos representadas las medidas del seno y del coseno del ángulo α.[br][br][img 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FHcbYIZoYvJ2LtYP1JOM557EUUUAXfEt5d2wsIbS5a3NzcbHkRVZgAjHjcCOoHatKw8z7DF5szzPjmRwoLfXaAPyFFFAGb4P/5Fe0+sn/obVt0UUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAGIT9q8aeXLyllZrLCvYO7MrN9cLgfU+tbdFFABRRRQAUUUUAFFFFABRRRQB//2Q==[/img][br][br]Por tanto, para el ángulo α el segmento rojo será la medida del seno y el segmento azul la medida[br]del coseno.[br]Podemos variar el punto A para observar la variación del seno y el coseno, así como para obtener cuándo cada uno de estos valores es positivo o negativo.[br]
Si utilizamos directamente la medida de los segmentos AC y OC, siempre serán positivos, por lo que no nos[br]sirven para que aparezcan con su signo correspondiente, según el ángulo esté en cada uno de los cuadrantes.[br]Para que aparezcan los valores correctos del seno y el coseno debemos utilizar las coordenadas del punto A.[br]En GeoGebra las coordenadas de un punto P se representan por [b](x(P),y(P))[/b], por lo que [b]x(P)[/b] hace referencia a la abscisa del punto P e [b]y(P)[/b] hace referencia al valor de la ordenada.[br]En la construcción que hemos realizado el seno del ángulo será y(A), mientras que el coseno será x(A). De esta forma, al cambiar el ángulo de cuadrante, las razones trigonométricas aparecerán con su signo correcto.
A continuación, aprovechando los valores que tenemos calculados del seno y del coseno vamos a representar estas funciones trigonométricas.[br]Para ello, definimos un punto cuyas coordenadas serán [b]([/b][b]α[/b][b], y(A))[/b]. La abscisa será el valor del[br]ángulo y la ordenada será el valor del seno de ese ángulo.[br]Aparecerá un punto D en la vista gráfica, al que cambiamos el color para que sea rojo.
Repitiendo el proceso para el coseno obtendremos la representación de la función correspondiente.

Information: Razones trigonométricas