【答案】
分析:先利用誘導(dǎo)公式把各個(gè)式子中角用銳角來(lái)表示,再根據(jù)正弦函數(shù)、余弦函數(shù)、正切函數(shù)在(0,
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/0.png)
)上的單調(diào)性,從而得出結(jié)論.
解答:解:由于sin
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/1.png)
=sin
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/2.png)
,sin
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/3.png)
=sin
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/4.png)
=sin
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/5.png)
,而且函數(shù)y=sinx在(0,
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/6.png)
)上是增函數(shù),故sin
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/7.png)
>sin
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/8.png)
,
∴
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/10.png)
,故A不正確.
由于cos(-1317°)=cos(-4×360°+123°)=cos123°=-cos57°,cos(-112°)=cos112°=-cos68°,而函數(shù)y=cosx在(0,
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/11.png)
)上是減函數(shù),
故cos68°<cos57°,即-cos68°>-cos57°,∴cos(-1317°)<cos(-112°),故B不正確.
由于
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/12.png)
=tan(-2π-
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/13.png)
)=-tan
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/14.png)
,tan(-
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/15.png)
)=tan(-5π-
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/16.png)
)=-tan
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/17.png)
,而函數(shù)y=tanx在(0,
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/18.png)
)上是增函數(shù),
故有tan
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/19.png)
>tan
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/20.png)
,∴-tan
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/21.png)
<-tan
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/22.png)
,即
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/23.png)
>
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/24.png)
,故C正確.
由于
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/25.png)
=tan(-2π-
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/26.png)
)=-tan
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/27.png)
,
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/28.png)
=tan(-5π-
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/29.png)
)=-tan
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/30.png)
,而函數(shù)y=tanx在(0,
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/31.png)
)上是增函數(shù),
故有tan
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/32.png)
>tan
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/33.png)
,∴-tan
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/34.png)
<-tan
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/35.png)
,即
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/36.png)
<
![](http://thumb.zyjl.cn//pic6/res/gzsx/web/STSource/20131202113021617863309/SYS201312021130216178633005_DA/37.png)
,故D不正確.
故選C.
點(diǎn)評(píng):本題主要考查正弦函數(shù)、余弦函數(shù)、正切函數(shù)在(0,π)上的單調(diào)性,誘導(dǎo)公式的應(yīng)用,屬于中檔題.