f(x)=cos(x+2/3π)+2cos²x/2,求值域,单调增区间.
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f(x)=cos(x+2/3π)+2cos²x/2,求值域,单调增区间.
f(x)=cos(x+2/3π)+2cos²x/2,求值域,单调增区间.
f(x)=cos(x+2/3π)+2cos²x/2,求值域,单调增区间.
若题目是f(x)=cos(x+2/3 π)+2 cos²x/2
则解为:
f(x)=-1/2cosx -2分之根号3 sinx + 1+cosx
=1/2cosx — 2分之根号3 sinx
=sin(x+ π/6)+1
因为sin(x+ π/6)∈【-1,1】
所以f(x)的值域为【0,2】
—π/2 +2kπ ≤ x+ π/6 ≤ π/2 +2kπ k∈Z
—3分之2π +2kπ≤ X ≤π/3 +2kπ
所以单调增区间为【—3分之2π +2kπ , π/3 +2kπ】