給出下列命題:
①函數(shù)y=sin(
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-2x)是偶函數(shù);
②函數(shù)y=sin(x+

)在閉區(qū)間[-
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,

]上是增函數(shù);
③直線x=

是函數(shù)y=sin(2x+

)圖像的一條對稱軸;
④將函數(shù)y=cos(2x-

)的圖像向左平移

個(gè)單位,得到函數(shù)y=cos2x的圖像.其中正確的命題的序號是________.
試題分析:①函數(shù)y=sin(

-2x)

,顯然是偶函數(shù),正確.
②

[-
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,
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],則

顯然不是函數(shù)y=sinx的增區(qū)間,所以y=sin(x+

)在閉區(qū)間[-
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,

]上是增函數(shù),錯(cuò).
③因?yàn)楫?dāng)x=
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時(shí),2x+

=

,所以直線x=

是函數(shù)y=sin(2x+

)圖像的一條對稱軸正確.
④將函數(shù)y=cos(2x-

)的圖像向左平移

個(gè)單位得到
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的圖像,因而此選項(xiàng)錯(cuò)誤,
故正確的命題序號為①③.
點(diǎn)評:本小題考查的知識點(diǎn)較多,一要知識三角誘導(dǎo)公式,二要知道三角函數(shù)圖像變換的規(guī)律:左加右減,上加下減.三要知道三角函數(shù)的性質(zhì),特別是對稱軸及對稱中心,單調(diào)區(qū)間,最值等.
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