已知函数f(x)=sinx平方+2倍根号3sin(x+派/4)cos(x-派/4)-cosx平方-根号3.1)求函数f(x)的最小正周期和单调递减区间2)求f(x)在(-派/12,25派/36)上的值域
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![已知函数f(x)=sinx平方+2倍根号3sin(x+派/4)cos(x-派/4)-cosx平方-根号3.1)求函数f(x)的最小正周期和单调递减区间2)求f(x)在(-派/12,25派/36)上的值域](/uploads/image/z/572393-65-3.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsinx%E5%B9%B3%E6%96%B9%2B2%E5%80%8D%E6%A0%B9%E5%8F%B73sin%28x%2B%E6%B4%BE%2F4%29cos%28x-%E6%B4%BE%2F4%29-cosx%E5%B9%B3%E6%96%B9-%E6%A0%B9%E5%8F%B73%EF%BC%8E1%29%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%E5%92%8C%E5%8D%95%E8%B0%83%E9%80%92%E5%87%8F%E5%8C%BA%E9%97%B42%29%E6%B1%82f%28x%29%E5%9C%A8%28-%E6%B4%BE%2F12%2C25%E6%B4%BE%2F36%29%E4%B8%8A%E7%9A%84%E5%80%BC%E5%9F%9F)
已知函数f(x)=sinx平方+2倍根号3sin(x+派/4)cos(x-派/4)-cosx平方-根号3.1)求函数f(x)的最小正周期和单调递减区间2)求f(x)在(-派/12,25派/36)上的值域
已知函数f(x)=sinx平方+2倍根号3sin(x+派/4)cos(x-派/4)-cosx平方-根号3.
1)求函数f(x)的最小正周期和单调递减区间
2)求f(x)在(-派/12,25派/36)上的值域
已知函数f(x)=sinx平方+2倍根号3sin(x+派/4)cos(x-派/4)-cosx平方-根号3.1)求函数f(x)的最小正周期和单调递减区间2)求f(x)在(-派/12,25派/36)上的值域
f(x)=(sinx)^2+2√3sin(x+π/4)cos(x-π/4)-(cosx)^2-√3
=-((cosx)^2-(sinx)^2)+√3(sin(x+π/4+x-π/4)+sin(x+π/4-(x-π/4))-√3
=-cos(2x)+√3sin(2x)+√3-√3
=√3sin(2x)-cos(2x)
=2sin(2x-π/6)
(1)
最小正周期:2π/2=π
单调递减区间:2kπ+π/2≤2x-π/6≤2kπ+3π/2
即kπ+π/3≤x≤kπ+5π/6 (k∈n)
(2)
-π/3
1、根据积化和差公式,
f(x)=(sinx)^2+2√3sin(x+π/4)cos(x-π/4)-(cosx)^2-√3
=-cos2x+√3[sin2x+sinπ/2)-√3
=2(√3sin2x/2-cos2x/2)
=2sin(2x-π/6),
最小正周期为2π/2=π,
2kπ+π/2<=2x-π/6<=2kπ+3π/2,
kπ+π...
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1、根据积化和差公式,
f(x)=(sinx)^2+2√3sin(x+π/4)cos(x-π/4)-(cosx)^2-√3
=-cos2x+√3[sin2x+sinπ/2)-√3
=2(√3sin2x/2-cos2x/2)
=2sin(2x-π/6),
最小正周期为2π/2=π,
2kπ+π/2<=2x-π/6<=2kπ+3π/2,
kπ+π/4<=x-π/12<=kπ+3π/4,
kπ+π/3<=x<=kπ+5π/6,
单调递减区间为:x∈[kπ+π/3,kπ+5π/6],(k∈Z),
2、单调递增区间为:x∈[kπ-5π/6,kπ+π/3],(k∈Z),
在区间(-π/12,25π/36)内,(-π/12,π/3)
为单调递增,最大值为2,最小为-√3,
(π/3,25π/36)内单调递减,最大为1,最小为2sin(2π/9),
故f(x)在(-π/12,25π/36)区间内值域:f(x)∈(-√3,2).
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