现将边长为2米的正方形铁片ABCD裁剪成一个半径为1米的扇形
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222810863407220/SYS201311012228108634072020_ST/0.png)
和一个矩形CRGP,如图所示,点E、F、P、R分别在AB、AD、BC、CD上,点G在
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222810863407220/SYS201311012228108634072020_ST/1.png)
上.设矩形CRGP的面积为S,∠GAE=θ,试将S表示为θ的函数,并指出点G在
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222810863407220/SYS201311012228108634072020_ST/2.png)
的何处时,矩形面积最大,并求之.
考点分析:
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可见cos3x可以表示为cosx的三次多项式.一般地,存在一个n次多项式P
n(t),使得cosnx=P
n(cosx),这些多项式P
n(t)称为切比雪夫多项式.
(I)求证:sin3x=3sinx-4sin
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(II)请求出P
4(t),即用一个cosx的四次多项式来表示cos4x;
(III)利用结论cos3x=4cos
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已知函数f(x)=2
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222810863407220/SYS201311012228108634072018_ST/0.png)
sinxcosx+2cos
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222810863407220/SYS201311012228108634072018_ST/1.png)
]上的最大值和最小值;
(Ⅱ)若f(x
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,x
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222810863407220/SYS201311012228108634072018_ST/3.png)
,
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222810863407220/SYS201311012228108634072018_ST/4.png)
],求cos2x
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已知
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222810863407220/SYS201311012228108634072017_ST/0.png)
,求:
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222810863407220/SYS201311012228108634072017_ST/1.png)
的值;
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![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222810863407220/SYS201311012228108634072017_ST/2.png)
的值;
(III)
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222810863407220/SYS201311012228108634072017_ST/3.png)
的值.
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定义在区间
![manfen5.com 满分网](http://img.manfen5.com/res/GZSX/web/STSource/20131101222810863407220/SYS201311012228108634072015_ST/0.png)
上的函数y=6cosx的图象与y=5tanx的图象的交点为P,过点P作PP
1⊥x轴于点P
1,直线PP
1与y=sinx的图象交于点P
2,则线段P
1P
2的长为
.
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