函数f(X)=sin2X+根号3cos2X(1) 将f(X)化为Asin(就是一般式的那个) (2)求出f(X)的最大值 最小值(3)求出f(X)的周期 (4) 求f(X)的单调区间请详细的讲解一下
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![函数f(X)=sin2X+根号3cos2X(1) 将f(X)化为Asin(就是一般式的那个) (2)求出f(X)的最大值 最小值(3)求出f(X)的周期 (4) 求f(X)的单调区间请详细的讲解一下](/uploads/image/z/2483152-16-2.jpg?t=%E5%87%BD%E6%95%B0f%28X%29%3Dsin2X%2B%E6%A0%B9%E5%8F%B73cos2X%EF%BC%881%EF%BC%89+%E5%B0%86f%28X%29%E5%8C%96%E4%B8%BAAsin%28%E5%B0%B1%E6%98%AF%E4%B8%80%E8%88%AC%E5%BC%8F%E7%9A%84%E9%82%A3%E4%B8%AA%EF%BC%89+%EF%BC%882%EF%BC%89%E6%B1%82%E5%87%BAf%28X%29%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC+%E6%9C%80%E5%B0%8F%E5%80%BC%EF%BC%883%EF%BC%89%E6%B1%82%E5%87%BAf%28X%29%E7%9A%84%E5%91%A8%E6%9C%9F+++++++++++%EF%BC%884%EF%BC%89+%E6%B1%82f%28X%EF%BC%89%E7%9A%84%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4%E8%AF%B7%E8%AF%A6%E7%BB%86%E7%9A%84%E8%AE%B2%E8%A7%A3%E4%B8%80%E4%B8%8B)
函数f(X)=sin2X+根号3cos2X(1) 将f(X)化为Asin(就是一般式的那个) (2)求出f(X)的最大值 最小值(3)求出f(X)的周期 (4) 求f(X)的单调区间请详细的讲解一下
函数f(X)=sin2X+根号3cos2X
(1) 将f(X)化为Asin(就是一般式的那个) (2)求出f(X)的最大值 最小值
(3)求出f(X)的周期 (4) 求f(X)的单调区间
请详细的讲解一下
函数f(X)=sin2X+根号3cos2X(1) 将f(X)化为Asin(就是一般式的那个) (2)求出f(X)的最大值 最小值(3)求出f(X)的周期 (4) 求f(X)的单调区间请详细的讲解一下
(1)f(X)=sin2X+√3cos2X=2(1/2sin2X+√3/2cos2X)=2(cosπ/3sin2x+sinπ/3cos2x)
=2sin(2x+π/3)
即f(x)=2sin(2x+π/3)
(2)∵-1≤sin(2x+π/3)≤1 ∴-2≤2sin(2x+π/3)≤2
∴函数的最大值为2,最小值为-2
(3)最小正周期为T=2π/2=π
(4)令2x+π/3=-π/2+2kπ 得x=-5π/12+kπ
-5π/12+kπ+π/2 = π/12+kπ (增加半个周期)
π/12+kπ +π/2=7π/12+kπ
∴函数的单调增区间为[-5π/12+kπ ,π/12+kπ ]
单调减区间为[π/12+kπ ,7π/12+kπ ]
(1):f(x)=2*(1/2sin2x+根号3/2cos2x)
=2*sin(2x+π/3)
(2):sin(2x+π/3)最大值为1 最小值为-1∴f(X)最大值为2,最小值为-2
(3):T=2π/W=2π/2=π
(4):f(x)取得最大值时sin(2x+π/3)=1∴2x=kπ+π/6
f(x)去的最小值时s...
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(1):f(x)=2*(1/2sin2x+根号3/2cos2x)
=2*sin(2x+π/3)
(2):sin(2x+π/3)最大值为1 最小值为-1∴f(X)最大值为2,最小值为-2
(3):T=2π/W=2π/2=π
(4):f(x)取得最大值时sin(2x+π/3)=1∴2x=kπ+π/6
f(x)去的最小值时sin(2x+π/3)=-1∴2x=kπ+7π/6
∴f(x)的单调区间为[{(k-1)π+7π/6}/2,(kπ+π/6)/2] ∪ [(Kπ+π/6)/2,(kπ+7π/6)/2]
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