tag:blogger.com,1999:blog-58579504019567077572024-03-20T22:03:06.086-07:00SECTOR CIRCULARjose garzonhttp://www.blogger.com/profile/16346783321699488575noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-5857950401956707757.post-34205880827364529122011-05-17T12:50:00.000-07:002011-05-17T12:50:38.057-07:00<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" dir="rtl" style="clear: both; text-align: center;"><span style="font-size: x-large;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/1TzGt3HX5bo?feature=player_embedded' frameborder='0'></iframe></span><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; text-align: left;"></div></div></div>jose garzonhttp://www.blogger.com/profile/16346783321699488575noreply@blogger.com0tag:blogger.com,1999:blog-5857950401956707757.post-61311514491392172632011-05-14T10:03:00.000-07:002011-05-19T15:25:10.267-07:00SECTOR CIRCULAR<div dir="ltr" style="text-align: left;" trbidi="on"><div style="text-align: left;"><span style="background-color: black; color: #f3f3f3; font-family: Georgia, "Times New Roman", serif; font-size: x-large;"><strong>SECTOR CIRCULAR</strong></span></div><div style="text-align: left;"><span style="background-color: black; color: #f3f3f3; font-family: Georgia, "Times New Roman", serif; font-size: large;"><strong>Se denomina sector circular a la porción de circulos comprendida entre un arco de circurferencia y sus respectivos radios delimitadores.</strong></span></div><div style="text-align: left;"><span class="mw-headline" id=".C3.81rea"><span style="background-color: black; color: #f3f3f3; font-family: Georgia, "Times New Roman", serif; font-size: x-large;"><strong>Área.</strong></span></span></div><div style="text-align: left;"><strong><span style="font-size: large;"><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black;"><span class="mw-headline"><span style="color: #f3f3f3;">El área de un sector circular depende de dos parámetros, el radio y el angulo central y está dada por la siguiente fórmula:</span></span><span style="color: #f3f3f3;"> </span></span></span></span></strong></div><span style="background-color: black; color: #cccccc;"></span><br />
<div class="separator" style="clear: both; text-align: left;"><span style="color: #990000; font-size: large; margin-left: 1em; margin-right: 1em;"><strong><span style="color: white;"><span style="background-color: black; font-family: Georgia, "Times New Roman", serif;"> <img alt="A = \pi r^2 \cdot \frac{\theta}{2 \pi} = \frac{r^2 \theta}{2}" class="tex" height="81" src="http://upload.wikimedia.org/math/9/7/d/97d612480aa18ced01bf0ad8352a431d.png" width="320" /></span></span></strong></span></div><span style="background-color: black; color: #f3f3f3;"></span><br />
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; text-align: left;"><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;"><span style="color: #f3f3f3;"><strong><span style="background-color: black; font-family: Georgia, "Times New Roman", serif; font-size: large;">Donde <img alt="r \," class="tex" src="http://upload.wikimedia.org/math/5/f/5/5f558fa7e9b1567daca23dc3433f5cec.png" /> es el radio de la circunferencia y <img alt="\theta \," class="tex" src="http://upload.wikimedia.org/math/1/f/0/1f09c25c5247c1eaf121df644ca42f8c.png" /> el ángulo que subtiende el arco de circunferencia, expresado en adianes...O también:</span></strong></span></div></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="background-color: black;"><br />
</span></div><a href="http://upload.wikimedia.org/math/4/e/c/4ecd3e21f4eb9186fdf0eb898a87db2d.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="background-color: black; color: #666666; font-family: Georgia, "Times New Roman", serif;"><img alt="A = \frac{\pi r^2 n^\circ }{360^\circ}" border="0" class="tex" height="93" src="http://upload.wikimedia.org/math/4/e/c/4ecd3e21f4eb9186fdf0eb898a87db2d.png" width="200" /></span></a><br />
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</span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="font-size: x-large;"><strong><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black;"> <span class="mw-headline" id="Area"><span style="color: #eeeeee;">Zona</span></span></span></span></strong></span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span class="mw-headline"><span style="color: #eeeeee;"><span style="font-size: large;"><strong><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black;">:El área total de un círculo es <span class="texhtml">π <i>r</i> <sup><span style="color: #eeeeee;">2</span></sup><span style="color: #eeeeee;">El área del sector se puede obtener multiplicando el círculo de la zona por la relación entre el ángulo y <span class="texhtml">2π</span> (porque el área del sector es proporcional al ángulo, y <span class="texhtml">2π</span> es el ángulo de todo el círculo): </span></span></span></span></strong></span></span></span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="background-color: black;"><br />
</span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black; color: #cccccc;"> <img alt="Un ^ r = \ pi 2 \ cdot \ frac {\ theta} {2 \ pi} = \ frac {r ^ 2 \ theta} {2}" class="tex" height="83" src="http://upload.wikimedia.org/math/9/7/d/97d612480aa18ced01bf0ad8352a431d.png" width="320" /></span></span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="background-color: black;"><br />
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<div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="color: #eeeeee;"><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black;"><strong><span style="font-size: large;">Convertir el ángulo central en </span></strong><span style="font-size: large;"><strong>grados</strong></span><strong><span style="font-size: large;"> se obtiene:</span></strong></span></span></span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="background-color: black;"><br />
</span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="background-color: black; color: #999999; font-family: Georgia, "Times New Roman", serif;"><img alt="Un ^ r = \ pi 2 \ cdot \ frac {\ theta ^ {\ circ}} {360}" class="tex" height="112" src="http://upload.wikimedia.org/math/4/3/c/43c310c8894ab52c766d0feab313ef5d.png" width="320" /></span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="background-color: black;"><br />
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</span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="color: #eeeeee; font-family: Georgia, "Times New Roman", serif; font-size: x-large;"><span class="mw-headline" id="Arc_length" style="background-color: black;"><strong>Longitud de arco:</strong></span></span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="background-color: black;"><br />
</span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="font-size: large;"><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black;"><span style="color: #eeeeee;"><strong>La longitud, <i><span class="texhtml">L,</span></i> del arco de un sector viene dada por:</strong></span> </span></span></span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="background-color: black;"><br />
</span></div><div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black;"> <span style="color: white;"> <span style="color: #666666;"><img alt="L = \ theta r \ cdot" class="tex" height="59" src="http://upload.wikimedia.org/math/5/3/0/530c6fad04008be67b3659480046fc1c.png" width="320" /></span></span></span></span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><a href="http://upload.wikimedia.org/math/b/e/8/be8933b478ea02e68e3ed4dc0326e4eb.png" imageanchor="1" style="clear: right; cssfloat: right; float: right; height: 28px; margin-bottom: 1em; margin-left: 1em; width: 482px;"><span style="background-color: black; font-family: Georgia, "Times New Roman", serif;"></span></a></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black;"><span style="color: #eeeeee; font-size: large;"><strong> donde <i>θ</i> está en radianes.</strong></span> </span></span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="background-color: black;"><br />
</span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black;"><span onmouseout="_tipoff()" onmouseover="_tipon(this)"> <span style="color: #eeeeee; font-size: large;"><strong>Si el ángulo se expresa en grados, entonces:</strong></span></span> </span></span></div><dl><dd><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black;"> <span style="color: white;"> <span style="color: #999999;"><img alt="L = \ theta ^ {\ circ} \ cdot R \ cdot \ frac {\ pi} {180}" class="tex" height="93" src="http://upload.wikimedia.org/math/a/2/3/a23c5e2d68b335233ae5493f2abfbb51.png" width="320" /></span></span></span></span></dd></dl><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="background-color: black; font-family: Georgia, "Times New Roman", serif;"> </span></div><h2><span style="background-color: black;"><span style="font-family: Georgia, "Times New Roman", serif;"><span onmouseout="_tipoff()" onmouseover="_tipon(this)"> <span class="mw-headline" id="Perimeter"><span style="color: #eeeeee; font-family: Georgia, "Times New Roman", serif; font-size: x-large;">Perímetro</span></span></span></span><span style="color: #eeeeee; font-family: Georgia, "Times New Roman", serif;"> </span></span></h2><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black;"><span onmouseout="_tipoff()" onmouseover="_tipon(this)"><span style="color: #eeeeee; font-family: Georgia, "Times New Roman", serif; font-size: large;"> <strong>La longitud del perimetro de un sector es la suma de la longitud del arco y los dos radios:</strong></span></span> </span></span><br />
<dl><dd><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black;"> <span style="color: #666666;"><img alt="P = L + 2r = \ theta r + 2r = r \ left (\ theta + 2 \ right)" class="tex" height="27" src="http://upload.wikimedia.org/math/b/e/8/be8933b478ea02e68e3ed4dc0326e4eb.png" width="400" /></span></span></span></dd></dl><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black;"><span onmouseout="_tipoff()" onmouseover="_tipon(this)"> <span style="color: #eeeeee; font-size: large;"><strong>donde <i>θ</i> está en radianes.</strong></span></span> </span></span><br />
<h2><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black;"><span onmouseout="_tipoff()" onmouseover="_tipon(this)"> <span class="mw-headline" id="Center_of_Mass"><span style="color: #eeeeee; font-size: x-large;">Centro de Masas</span></span></span> </span></span></h2><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black;"><span onmouseout="_tipoff()" onmouseover="_tipon(this)"> <span style="color: #eeeeee; font-size: large;"><strong>La distancia desde el centro del círculo (que el sector es una parte) del centro de masa del sector es el cociente de 4 radios y pi 3:</strong></span></span><span style="color: #eeeeee; font-size: large;"><strong> </strong></span></span></span><br />
<dl><dd><span style="font-family: Georgia, "Times New Roman", serif;"><span style="background-color: black;"> <span style="color: #666666;"><img alt="\ Bar {r} = \ frac {4r} {3 \ pi}" class="tex" height="136" src="http://upload.wikimedia.org/math/3/8/1/3812a49828cf1744c5a44560ba2d3f68.png" width="200" /></span></span></span></dd></dl><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="background-color: black; font-family: Georgia, "Times New Roman", serif;"> </span></div><div class="separator" style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; clear: both; text-align: left;"><span style="background-color: black;"><br />
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<span style="background-color: black;"></span></span></div><strong><span style="background-color: black; font-size: large;"></span></strong></div>jose garzonhttp://www.blogger.com/profile/16346783321699488575noreply@blogger.com0