6:若函数f(x)=asin(x+3分之π)+sin(x-6分之π)是偶函数,则a的值为多少

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/15 10:07:32
6:若函数f(x)=asin(x+3分之π)+sin(x-6分之π)是偶函数,则a的值为多少
x)3zѽigS7iTh&giTh?h{|6X@ .l ZtvL|>iÞ';v=]2醉6IE0VΆf}v=Ldc7L4*taJt"+M3ԅgi 5:^ sظbbD ("$tf+jƧ n~[]#$M`O|{{uLxt׌/VQ,c<;hڀ9/Fѳ;oI @:

6:若函数f(x)=asin(x+3分之π)+sin(x-6分之π)是偶函数,则a的值为多少
6:若函数f(x)=asin(x+3分之π)+sin(x-6分之π)是偶函数,则a的值为多少

6:若函数f(x)=asin(x+3分之π)+sin(x-6分之π)是偶函数,则a的值为多少
答:
f(x)=asin(x+π/3)+sin(x-π/6)
f(-x)=asin(-x+π/3)+sin(-x-π/6)
=-asin(x-π/3)-sin(x+π/6)=f(x)
=asin(x+π/3)+sin(x-π/6)
所以:
-asinxcosπ/3+acosxsinπ/3-sinxcosπ/6-cosxsinπ/6
=asinxcosπ/3+acosxsinπ/3+sinxcosπ/6-cosxsinπ/6
所以:2asinxcosπ/3=-2sinxcosπ/6
对任意x都成立,则有:
acosπ/3=-cosπ/6
a=-√3

负的根号三