文档介绍：第一课时正弦函数、余弦函数的性质 Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 问题提出 1. 正弦函数和余弦函数的图象分别是什么?二者有何相互联系? y-1 x O1π2π 3π4π 5π6π-2π-3π-4π-5π-6π-πy=sinx x yO 1-1 2 ?2 ?? 2 ??2 ?? 2 ??2 ??? 2 ??2 ??? 2 ???2 ??? 2 ???2 ????y=cosx Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. “周而复始”的变化规律,如年有四季更替,月有阴晴圆缺. 这种现象在数学上称为周期性, 在函数领域里,周期性是函数的一个重要性质. Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 知识探究(一): 周期函数的概念思考 1: 由正弦函数的图象可知, 正弦曲线每相隔 2π个单位重复出现, 这一规律的理论依据是什么? sin( 2 ) sin ( ) x k x k Z ?? ??.思考 2:设f(x)=sinx ,则可以怎样表示?其数学意义如何? sin( 2 ) sin x k x ?? ? Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd. 思考 3: 为了突出函数的这个特性,我们把函数 f(x)=sinx 称为周期函数,2kπ为这个函数的周期. 一般地,如何定义周期函数? 对于函数 f(x) ,如果存在一个非零常数 T ,使得当x 取定义域内的每一个值时,都有 f(x+T)=f(x) , 那么函数 f(x) 就叫做周期函数,非零常数 T 就叫做这个函数的周期. Evaluation only. Evaluation only. Created with Client Profile . Created with Client Profile . Copyright 2004-2011 Aspose Pty Ltd. Copyright 2004-2011 Aspose Pty Ltd