1 . 余弦函数
的性质
(1)余弦函数
的周期为_______ ,最小正周期为_______ .余弦型函数
的最小正周期为______
(2)余弦函数
为_______ (在奇函数、偶函数、非奇非偶函数中选择),正弦曲线
的对称轴方程为_______ ,对称中心为_______ .
(3)余弦函数
的单调增区间为_______ ;单调减区间为_________ ,值域为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f3ef6df936720af6d46996d2bd65cf.png)
(1)余弦函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f3ef6df936720af6d46996d2bd65cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09c906d680a9a908b380f69abc38258.png)
(2)余弦函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f3ef6df936720af6d46996d2bd65cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368f98c3347730612ca1992a2b1fdeb1.png)
(3)余弦函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f3ef6df936720af6d46996d2bd65cf.png)
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2 . 一般地,对于指数函数
与一次函数
,随着
的增大,一次函数
保持固定的增长速度,而
增长越_______ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbe323771bc92bf5767e1bd9a46b946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e2b6466242aec6c1ff38f83eb66314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19e2b6466242aec6c1ff38f83eb66314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbe323771bc92bf5767e1bd9a46b946.png)
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3 . 二分法
对于区间
上图象连续不断其
的函数
,通过不断地把它的零点所在区间_____ ,使所得区间的两个端点逐步逼近零点,进而得到零点近似值的方法称为二分法.
对于区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/563ae8f3e5fedd32ee82ab16f0279bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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4 . 二分法的一般步骤(精确度为
)
(1)确定零点
所在区间为
,验证________ ;
(2)求区间
的____
;
(3)计算
;
①若____ ,则
就是函数的零点;
②若_____ ,则
,令
;
③若_____ ,则
,令
;
(4)判断是否达到精确度:若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babb4fcca2ad56908b79fe23fb7b2466.png)
_____ ,则得到零点近似值
(或
),否则重复步骤(2)-(4).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711c92626a97e6b778b3aa86e663ee97.png)
(1)确定零点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
(2)求区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(3)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee0882f5f575d9e0ae7677efbd41b38.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8267135d61ec0f62afb4245b6203bc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05d3b8f5c9df891ef6fbcaf12f43207.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8951566d2bba8746fdeeccdfdfee8db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759b29a7b2b3735306f1a650355a7858.png)
(4)判断是否达到精确度:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babb4fcca2ad56908b79fe23fb7b2466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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2023-08-09更新
|
176次组卷
|
3卷引用:第2课时 课前 用二分法求方程的近似解
23-24高一上·江苏·课后作业
5 . 一般地,对于函数
,我们把使______ 的实数
称为函数
的零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
您最近一年使用:0次
2023-08-09更新
|
76次组卷
|
3卷引用:第1课时 课前 函数的零点
23-24高一上·江苏·课后作业
6 . 零点存在定理:如果函数
在
上的图象是一条______ 的曲线,且有______ ,那么函数
在
内至少存在一个零点
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920f30b69a2f0634b0ddc39ef2704b81.png)
您最近一年使用:0次
23-24高一上·江苏·课后作业
7 . 函数与方程的关系:方程
有实数解
函数
有零点_____
函数
的图象与
轴有公共点_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f53e1c26ca8e40cdbb7c959932cdc85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39c662a3927de39135c3eee4b9cb68f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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8 . 弧度制
我们规定:长度等于_______ 的圆弧所对的圆心角叫做1弧度的角,弧度的单位用符号_____ 表示,读作弧度.
我们规定:长度等于
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9 . 弧长公式和扇形面积公式
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050294162a78c6f4d6a87849bd3049a3.png)
______ ;
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/779e65b968d7d16957f734f3a9d39550.png)
______ ;(
为扇形圆心角的弧度数)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050294162a78c6f4d6a87849bd3049a3.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/779e65b968d7d16957f734f3a9d39550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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10 . 角度与弧度制的换算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5106c18ff93855989da9400a2b76ed3.png)
_____ ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c3b6143b54eaf6be9f40aa5159aeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1d9c2b0e533e8528be255d58507e4e9.png)
______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5106c18ff93855989da9400a2b76ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c3b6143b54eaf6be9f40aa5159aeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1d9c2b0e533e8528be255d58507e4e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a978d42e7546ccb688b556c7bc4a7f13.png)
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