解题方法
1 . 正弦信号是频率成分最为单一的信号,复杂的信号,例如电信号,都可以分解为许多频率不同、幅度不等的正弦型信号的叠加.正弦信号的波形可以用数学上的正弦型函数来描述:
,其中
表示正弦信号的瞬时大小电压V(单位:V)是关于时间t(单位:s)的函数,而
表示正弦信号的幅度,
是正弦信号的频率,相应的
为正弦信号的周期,
为正弦信号的初相.由于正弦信号是一种最简单的信号,所以在电路系统设计中,科学家和工程师们经常以正弦信号作为信号源(输入信号)去研究整个电路的工作机理.如图是一种典型的加法器电路图,图中的三角形图标是一个运算放大器,电路中有四个电阻,电阻值分别为
,
,
,
(单位:Ω).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/10/bafe7d46-ad02-484e-bbe0-0ce32055343d.png?resizew=255)
和
是两个输入信号,
表示的是输出信号,根据加法器的工作原理,
与
和
的关系为:
.
例如当
,输入信号
,
时,输出信号:
.
(1)若
,输入信号
,
,则
的最大值为___________;
(2)已知
,
,
,输入信号
,
.若
(其中
),则
___________;
(3)已知
,
,
,且
,
.若
的最大值为
,则满足条件的一组电阻值
,
分别是_____________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b5219b4b23a36899bc29cb18b22903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ac562e5ac2ebbc5982b4e2e20e88a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13378be06b6b01bcad1d261ff14e87cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a16d6967d4b35fd028264b5b4c9459b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efc18a5bb2e53586331b2a58538a48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f20f21a9d50b61dac519a3ddab539d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2c4640b2bee411935f588fc5433c74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e2599548b7b123f3c8d0b91aacd5de.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/10/bafe7d46-ad02-484e-bbe0-0ce32055343d.png?resizew=255)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61359b33f8d3d33e07adcaf28116b197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5137a145c21f194bef7a7ec110a9de6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68894d53f9274ba54a34e3c485fb34e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68894d53f9274ba54a34e3c485fb34e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61359b33f8d3d33e07adcaf28116b197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5137a145c21f194bef7a7ec110a9de6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9731ce70ad342274d2a1bdef18b25578.png)
例如当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a450b44cb8e6ff7c8410396352d363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54cd40b19ff105a0387ee58765155477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4292cad692a0322fa9fb3c5932836658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45cacbe9bf09e8345c6ffd37d18df12.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a450b44cb8e6ff7c8410396352d363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54cd40b19ff105a0387ee58765155477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4292cad692a0322fa9fb3c5932836658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68894d53f9274ba54a34e3c485fb34e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1bde887662bc9bed664b5f9c151529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dd7252bd86ce2d11eb387e0f4962b21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f950eccff894fce3c80b64897146fc44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8919d57fa1689a400edc62872779d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ce55f98ba86201271588a1289a0111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/206507b4e17e272d7a80e996b98e3b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13378be06b6b01bcad1d261ff14e87cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8225d0531fba46cbb4a3af4dd2d6751f.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f33d476e37e70f7c720386dfdbd1f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ff5385ac347af2c612009d412c00b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/757d05fcbfea8e925ed5382dbd051fa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54cd40b19ff105a0387ee58765155477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db087e0f05028cf086902dcc0784e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68894d53f9274ba54a34e3c485fb34e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efc18a5bb2e53586331b2a58538a48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f20f21a9d50b61dac519a3ddab539d.png)
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4卷引用:北京市海淀区2021-2022学年高一下学期期末练习数学试题
北京市海淀区2021-2022学年高一下学期期末练习数学试题重庆市北碚区2023届高三上学期10月月度质量检测数学试题(已下线)5.7三角函数的应用(分层作业)-【上好课】(已下线)5.7三角函数的应用(导学案)-【上好课】
名校
2 . 若函数
满足
且
,则称函数
为“
函数”.
(1)试判断
是否为“
函数”,并说明理由;
(2)函数
为“
函数”,且当
时,
,求
的解析式,并写出在
上的单调递增区间;
(3)在(2)的条件下,当
时,关于
的方程
(
为常数)有解,记该方程所有解的和为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28d61f63c51f3b3ec2ee91f24ffcac6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/744a94ace87e4e7499a3402063b74e41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a185071eb029625e2c6d349e021168b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d30b193d1befc87b1a2a400e39b9b4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92c54181785770c2703083617cc1a6c6.png)
(3)在(2)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1265eb1ec8d5d6c56a8b25a76b5bbbe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8bfd47b7c68564110c720e9246a02ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba8de1f13e31dbf101d796867ac375d.png)
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