题目内容
在直角坐标平面的第一象限内有一点P(x,4),点O是原点,∠α是OP与x轴的正半轴的夹角.如果cosα=0.6,那么下列各直线中,不经过点P的是( )A.y=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_ST/0.png)
B.y=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_ST/1.png)
C.y=2x-2
D.y=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_ST/2.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_ST/3.png)
【答案】分析:过P作PA⊥x轴于A,根据余弦的定义得到cosα=
=0.6=
,设OA=3a,则OP=5a,在Rt△OAP中,根据勾股定理有(5a)2=42+(3a)2,可解得a=1,即可确定P点坐标为(3,4),然后把P(3,4)分别代入四个一次函数的解析式中,再根据“若点的坐标满足一次函数的解析式,则这个点一定在其图象上”进行判断即可.
解答:解:过P作PA⊥x轴于A,如图,![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_DA/images2.png)
∵P(x,4),∠α是OP与x轴的正半轴的夹角,cosα=0.6,
∴cosα=
=0.6=
,
设OA=3a,则OP=5a,
在Rt△OAP中,PA=4,OP2=PA2+OA2,即(5a)2=42+(3a)2,解得a=1,
∴OA=3,
∴P点坐标为(3,4),
当x=3时,y=
x=4,所以P点在直线y=
x上;
当x=3时,y=
x=
≠4,所以P点在直线y=
x上;
当x=3时,y=2x-2=4,所以P点在直线y=2x-2上;
当x=3时,y=
x+
=4,所以P点在直线y=
x+
上.
故选B.
点评:本题考查了一次函数图象上点的坐标特点:若点的坐标满足一次函数的解析式,则这个点一定在其图象上.也考查了解直角三角形.
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_DA/0.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_DA/1.png)
解答:解:过P作PA⊥x轴于A,如图,
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_DA/images2.png)
∵P(x,4),∠α是OP与x轴的正半轴的夹角,cosα=0.6,
∴cosα=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_DA/2.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_DA/3.png)
设OA=3a,则OP=5a,
在Rt△OAP中,PA=4,OP2=PA2+OA2,即(5a)2=42+(3a)2,解得a=1,
∴OA=3,
∴P点坐标为(3,4),
当x=3时,y=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_DA/4.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_DA/5.png)
当x=3时,y=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_DA/6.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_DA/7.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_DA/8.png)
当x=3时,y=2x-2=4,所以P点在直线y=2x-2上;
当x=3时,y=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_DA/9.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_DA/10.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_DA/11.png)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131022164818765838090/SYS201310221648187658380017_DA/12.png)
故选B.
点评:本题考查了一次函数图象上点的坐标特点:若点的坐标满足一次函数的解析式,则这个点一定在其图象上.也考查了解直角三角形.
![](http://thumb2018.1010pic.com/images/loading.gif)
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