解题方法
1 . 已知函数
的最小正周期为
,给出以下结论:
①
在区间
上的值域为
;
②
在区间
上单调递减;
③将
的图象向左平移
个单位长度,所得图象对应的函数
为偶函数;
④
在区间
内的所有零点之和为
.
其中所有正确结论的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ce723544931d74e4c800b947ab9176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592adec197b57a7a9695e358199f1180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3407bce8ef91b09ef5f75714ed3e6a5e.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb935734bfd51c3338f223934a668e29.png)
③将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca83bfb0e8dd7435711711f1a209ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d91a5d6489c77f68da4024051762e74.png)
其中所有正确结论的序号为( )
A.①③ | B.②④ | C.②③④ | D.①②④ |
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2 . 判断正误(正确的填写“正确”,错误的填写“错误”)
(1)两角和与差的正弦、余弦公式中的角α,β是任意的.( )
(2)存在
,使得
成立.( )
(3)对于任意
,
都不成立.( )
(4)
.( )
(1)两角和与差的正弦、余弦公式中的角α,β是任意的.
(2)存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7170baf4e8fc6bf3dd518cc49bf736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b839269b506f3abcf4458ecd3a8cfd.png)
(3)对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7170baf4e8fc6bf3dd518cc49bf736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/649c3008c4545c195e0f279606f881c9.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75124fba8b95791947cf8eff99a84630.png)
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3 . 判断正误(正确的写正确,错误的写错误)
(1)半角公式对任意角都适用.( )
(2)
.( )
(3)对于任意
,
都不成立.( )
(4)
.( )
(1)半角公式对任意角都适用.
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82418104ff528cd594f390f51c569e6c.png)
(3)对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9883e09b1ac40ccaebcaec21e2871c56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/996e0d157addb2a025b2438ddda8e067.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/173d65ac02a841a07d30b5136b8d9c4d.png)
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4 . 给出集合
.
(1)若
,求证:函数
;
(2)由(1)分析可知,
是周期函数且是奇函数,于是张三同学得出两个命
题:命题甲:集合
中的元素都是周期函数.命题乙:集合
中的元素都是奇函数. 请对此
给出判断,如果正确,请证明;如果不正确,请举反例;
(3)若
,数列
满足:
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
,数列
的前
项
和为
,试问是否存在实数
、
,使得任意的
,都有
成立,若
存在,求出
、
的取值范围,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2797a0dde20f22497c6190d08c71b741.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c6d8eccab2b897f45885ed81195248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5314a9d2205a2beba0dcffb8fd943b18.png)
(2)由(1)分析可知,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c6d8eccab2b897f45885ed81195248.png)
题:命题甲:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
给出判断,如果正确,请证明;如果不正确,请举反例;
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96f3ea0467dc6393d7c4b602175a394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5fb8208a95205a6437385ba884547a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
和为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab958eede2dbad749ba70bb230c88fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5014429b696a37a9461b66f22b1800.png)
存在,求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
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