高中数学任意角课件新人教必修

1.1任意角Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd. 初中角的定义：从一个点出发引出的两条射线构成的几何图形“旋转”形成角角：一条射线绕着它的端点在平面内旋转形成的图形1、角的范围oAB始边终边顶点Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd. 2、花样游泳中，运动员旋转的周数如何用角度计算来表示？3、汽车在前进和倒车中，车轮转动的角度如何表示才比较合理？4、工人在拧紧或拧松螺丝时，转动的角度如何表示才比较合适？Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd. 定义：正角：按逆时针方向旋转形成的角负角：按顺时针方向旋转形成的角零角：一条射线没有作任何旋转形成的角任意角Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd. 终边终边B1B2Aα=210°β=-150°Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd. xyo始边终边1)置角的顶点于原点终边落在第几象限就是第几象限角2)始边重合于x轴的正半轴AB1B2Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd. xyo3003900=300+3600－3300=300－3600300=300+0x3600与α终边相同的角的一般形式为α＋k3600，k∈ZS={β|β=α+k360°,k∈Z}所有与角α终边相同的角，连同角α在内，可构成一个集合即任一与角α终边相同的角，都可以表示成角α与整数个周角的和。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd. 例1把下列各角写成α＋k3600（00≤ａ＜3600，ｋ∈ｚ）的形式，并判定它们分别是第几象限角。(1)–120°;(2)640°；(3)-950°12′。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd. 例2写出终边落在y轴上的角的集合。终边落在坐标轴上的情形xyo0090018002700+k360°+k360°+k360°+k360°或3600＋k360°Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd. 解：终边落在ｙ轴正半轴上的角的集合为S1={β|β=900+k∙3600,k∈Z}={β|β=900+2k·1800,k∈Z}终边落在ｙ轴负半轴上的角的集合为S2={β|β=2700+k∙3600,k∈Z}={β|β=900+(2k+1)·1800,k∈Z}S=S1∪S2所以　终边落在ｙ轴上的角的集合为={β|β=900+n∙1800，n∈Z}xyO900+k∙36002700+k∙3600Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd. 练习1一角为300，其终边按顺时针方向旋转三周后的角度数是。逆时针呢？2集合M={a|a=k900,kZ}中，各角的终边都在。3与-17780的终边相同且绝对值最小的角是。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd. 例3：写出与下列各角终边相同的角的集合S并把S中适合-3600到7200的元素找出来：（1）700（2）-210（3）463014'例4、写出终边在直线y=x上的角的集合S，并把S中适合不等式-360°≤β＜720°的元素写出来。xyOEvaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.