已知函数f(x)=sin(x+π/6)+sin(x-π/6)-2cos^2(x/2),x∈[0,π] 求化简函数f(x)
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已知函数f(x)=sin(x+π/6)+sin(x-π/6)-2cos^2(x/2),x∈[0,π] 求化简函数f(x)的解析式,
(2)求函数f(x)的最大值及相应的自变量x的取值,
(2)求函数f(x)的最大值及相应的自变量x的取值,
![已知函数f(x)=sin(x+π/6)+sin(x-π/6)-2cos^2(x/2),x∈[0,π] 求化简函数f(x)](/uploads/image/z/16196809-49-9.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%29-2cos%5E2%28x%2F2%29%2Cx%E2%88%88%5B0%2C%CF%80%5D+%E6%B1%82%E5%8C%96%E7%AE%80%E5%87%BD%E6%95%B0f%28x%29)
f(x)=sin(x+π/6)+sin(x-π/6)-2cos^2(x/2)=2sinxcosπ/6-(1+cosx)=根号3sinx-cosx-1
=2(sinx根号3/2-1/2cosx)-1=2sin(x-π/6)-1
f(x)=2sin(x-π/6)-1
x∈[0,π],x-π/6∈[-π/6,5/6π],
当x=2/3π时,sinx-π/6=1,f(x)取得最大值=1
当x=0时,sin-π/6=-1/2,f(x)取得最小值=-2
=2(sinx根号3/2-1/2cosx)-1=2sin(x-π/6)-1
f(x)=2sin(x-π/6)-1
x∈[0,π],x-π/6∈[-π/6,5/6π],
当x=2/3π时,sinx-π/6=1,f(x)取得最大值=1
当x=0时,sin-π/6=-1/2,f(x)取得最小值=-2
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