已知函数f(x)=-根号3sin²x+sinxcosx已知函数f(x)=-根号3sin²x+sinxcosx(1)求f(25π/6)(2)设α∈(0,π),f(α/2)=1/4-根号3/2,求sinα的值
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![已知函数f(x)=-根号3sin²x+sinxcosx已知函数f(x)=-根号3sin²x+sinxcosx(1)求f(25π/6)(2)设α∈(0,π),f(α/2)=1/4-根号3/2,求sinα的值](/uploads/image/z/1791174-30-4.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D-%E6%A0%B9%E5%8F%B73sin%26%23178%3Bx%2Bsinxcosx%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D-%E6%A0%B9%E5%8F%B73sin%26%23178%3Bx%2Bsinxcosx%EF%BC%881%EF%BC%89%E6%B1%82f%EF%BC%8825%CF%80%2F6%EF%BC%89%EF%BC%882%EF%BC%89%E8%AE%BE%CE%B1%E2%88%88%EF%BC%880%2C%CF%80%EF%BC%89%2Cf%EF%BC%88%CE%B1%2F2%EF%BC%89%3D1%2F4-%E6%A0%B9%E5%8F%B73%2F2%2C%E6%B1%82sin%CE%B1%E7%9A%84%E5%80%BC)
已知函数f(x)=-根号3sin²x+sinxcosx已知函数f(x)=-根号3sin²x+sinxcosx(1)求f(25π/6)(2)设α∈(0,π),f(α/2)=1/4-根号3/2,求sinα的值
已知函数f(x)=-根号3sin²x+sinxcosx
已知函数f(x)=-根号3sin²x+sinxcosx
(1)求f(25π/6)
(2)设α∈(0,π),f(α/2)=1/4-根号3/2,求sinα的值
已知函数f(x)=-根号3sin²x+sinxcosx已知函数f(x)=-根号3sin²x+sinxcosx(1)求f(25π/6)(2)设α∈(0,π),f(α/2)=1/4-根号3/2,求sinα的值
f(x)=-√3/2(1-cos2x)+1/2sin2x
=-√3/2+sin(2x+π/3)
f(25π/6)=-√3/2+sin(2*25π/6+π/3)=0
2、f(α/2)=1/4-√3/2==-√3/2+sin(2*α/2+π/3)
sin(α+π/3)=1/4
因为α∈(0,π),所以α=π-acrsin1/4-π/3=2π/3-arcsin1/4
所以sinα=sin(2π/3-arcsin1/4)=√3/2*√15/4-1/2*1/4=3√5/8-1/8
(1)f(x)=-√3(1-cos2x)/2+1/2sin2x=√3/2*cos2x+1/2sin2x -√3/2
=sinπ/3cos2x+cosπ/3sin2x -√3/2=sin(2x+π/3) -√3/2
周期π f(25π/6)=f(π/6)=sin(2π/3) -√3/2=0
(2)f(a/2)=si...
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(1)f(x)=-√3(1-cos2x)/2+1/2sin2x=√3/2*cos2x+1/2sin2x -√3/2
=sinπ/3cos2x+cosπ/3sin2x -√3/2=sin(2x+π/3) -√3/2
周期π f(25π/6)=f(π/6)=sin(2π/3) -√3/2=0
(2)f(a/2)=sin(a+π/3) -√3/2= 1/4-√3/2
sin(a+π/3)=1/4 , α∈(0,π)可得出,a在第二象限,cos(a+π/3)=-√15/4
sina=sin[(a+π/3)-π/3]=sin(a+π/3)cosπ/3-cos(a+π/3)sinπ/3=1/8+3√5/8
刚做错了抱歉哈
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