已知函数f(X)=4sin的2次方x+4根号3sinxcosx-31.求f(X)的最小正周期2.求f(x)的单调增区间3若.x属于{0,π/2},求f(x)的最大值和最小值,(过程,谢谢)
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![已知函数f(X)=4sin的2次方x+4根号3sinxcosx-31.求f(X)的最小正周期2.求f(x)的单调增区间3若.x属于{0,π/2},求f(x)的最大值和最小值,(过程,谢谢)](/uploads/image/z/8712099-27-9.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28X%29%3D4sin%E7%9A%842%E6%AC%A1%E6%96%B9x%2B4%E6%A0%B9%E5%8F%B73sinxcosx-31.%E6%B1%82f%28X%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F2.%E6%B1%82f%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E5%A2%9E%E5%8C%BA%E9%97%B43%E8%8B%A5.x%E5%B1%9E%E4%BA%8E%7B0%2C%CF%80%2F2%7D%2C%E6%B1%82f%28x%29%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E5%92%8C%E6%9C%80%E5%B0%8F%E5%80%BC%2C%EF%BC%88%E8%BF%87%E7%A8%8B%2C%E8%B0%A2%E8%B0%A2%EF%BC%89)
已知函数f(X)=4sin的2次方x+4根号3sinxcosx-31.求f(X)的最小正周期2.求f(x)的单调增区间3若.x属于{0,π/2},求f(x)的最大值和最小值,(过程,谢谢)
已知函数f(X)=4sin的2次方x+4根号3sinxcosx-3
1.求f(X)的最小正周期
2.求f(x)的单调增区间
3若.x属于{0,π/2},求f(x)的最大值和最小值,
(过程,谢谢)
已知函数f(X)=4sin的2次方x+4根号3sinxcosx-31.求f(X)的最小正周期2.求f(x)的单调增区间3若.x属于{0,π/2},求f(x)的最大值和最小值,(过程,谢谢)
f(x)=4(sinx)^2+4√3sinxcosx-3
=2(1-cos2x)+2√3sin2x-3
=2√3sin2x-2cos2x-1
=4(√3/2sin2x-1/2cos2x)-1
=4(sin2xcos(π/6)-cos2xsin(π/6))-1
=4sin(2x-π/6)-1
所以
1.f(x)的最小正周期是 2π/2=π
2.f(x)=4sin(2(x-π/12))-1
所以单调增区别是 [kπ-π/4+π/12,kπ+π/4+π/12]
即 [kπ-π/6,kπ+π/3] k∈Z
3.当x ∈[0,π/2]时
f(x)=4sin(2x-π/6))-1
显然,在 -π/6
(sinx)^2=1/2-cos(2x)/2
f(X)=4sin的2次方x+4根号3sinxcosx-3=
=(2-2cos(2x))+2sin(2x)-3=
=2(sin(2x)-cos(2x))-1=
=2sqrt(2)sin(2x-π/4)-1
1.f(X)的最小正周期为π
2.f(x)的单调增区间(2kπ-π/8,2kπ+7π/8)
3若.x属于{0,π/2},f(x)的最大值为2sqrt(2)-1,最小值为-3