已知函数f(x)=sin(x+π/6)+sin(x-π/6)+cosx+a(a属于R,a是常数)(1)求函数f(x)的最小正周期(2)若x属于[-π/2,π/2]时,最大值最小值之和为√3,求a的值.
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![已知函数f(x)=sin(x+π/6)+sin(x-π/6)+cosx+a(a属于R,a是常数)(1)求函数f(x)的最小正周期(2)若x属于[-π/2,π/2]时,最大值最小值之和为√3,求a的值.](/uploads/image/z/1488405-21-5.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin%28x%2B%CF%80%2F6%29%2Bsin%28x-%CF%80%2F6%29%2Bcosx%2Ba%28a%E5%B1%9E%E4%BA%8ER%2Ca%E6%98%AF%E5%B8%B8%E6%95%B0%29%EF%BC%881%EF%BC%89%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%EF%BC%882%EF%BC%89%E8%8B%A5x%E5%B1%9E%E4%BA%8E%5B-%CF%80%2F2%2C%CF%80%2F2%5D%E6%97%B6%2C%E6%9C%80%E5%A4%A7%E5%80%BC%E6%9C%80%E5%B0%8F%E5%80%BC%E4%B9%8B%E5%92%8C%E4%B8%BA%E2%88%9A3%2C%E6%B1%82a%E7%9A%84%E5%80%BC.)
已知函数f(x)=sin(x+π/6)+sin(x-π/6)+cosx+a(a属于R,a是常数)(1)求函数f(x)的最小正周期(2)若x属于[-π/2,π/2]时,最大值最小值之和为√3,求a的值.
已知函数f(x)=sin(x+π/6)+sin(x-π/6)+cosx+a(a属于R,a是常数)
(1)求函数f(x)的最小正周期
(2)若x属于[-π/2,π/2]时,最大值最小值之和为√3,求a的值.
已知函数f(x)=sin(x+π/6)+sin(x-π/6)+cosx+a(a属于R,a是常数)(1)求函数f(x)的最小正周期(2)若x属于[-π/2,π/2]时,最大值最小值之和为√3,求a的值.
1、
f(x)=sinxcosπ/6+cosxsinπ/6+sinxcosπ/6-cosxsinπ/6+cosx+a
=2sinxcosπ/6+cosx+a
=√3sinx+cosx+a
=√[(√3)²+1²]sin(x+z)+a
=2sin(x+z)+a
其中tanz=1/√3
所以T=2π/1=2π
2、
tanz=1/√3
z=π/6
f(x)=2sin(x+π/6)+a
-π/2
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