已知函数f(x)=√3sinxcosx+봀cos2x 求f(x)函数的最小正周期 求f(x)函数的单调递增区间

2025-02-19 09:20:28
推荐回答(2个)
回答(1):

f(x)=√3sinxcosx+½cos2x=√3/2sin2x+½cos2x=sin(2x+π/6)
最小正周期是2π/2=π
单增区间令-π/2+2kπ≤2x+π/6≤π/2+2kπ解得区间为
[-π/3+kπ,π/6+kπ]

回答(2):

函数f(x)= 2√3sinxcosx +2(cosx的)^ 2-1 =根号3sin2x + cos2x = 2sin(2X + PAI / 6)
最小正周期为T = 2Pai / 2 =排

单调递减区间是2kPai +排/ 2 <= 2X +排/ 6 <=排2kPai +3 / 2
:[KPAI + PAI / 6 +2排KPAI / 3]