已知向量a=(sinX,1),b=(cosX,负的二分之一 求函数f(x)=a.(2b-a)+cos二次方x的单调增区间求
已知向量a=(sinX,1),b=(cosX,负的二分之一 求函数f(x)=a.(2b-a)+cos二次方x的单调增区间
求
f(x)=2ab-a²+cos²x=2(sinxcosx-1/2)+(cos2x+1)/2=sin2x+cos2x-1/2=根号2sin(2x+π/4)-1/2
单调增区间为：2kπ-π/2kπ-3π/8
如果详细一点的话就是令2x=t原式=sint+cost-1/2=根号2sin(t+π/4)-1/2
令t+π/4=u 则单调增区间为u属于（2kπ-π/2，2kπ+π/2）即x属于（kπ-3π/8,kπ+π/8）
f(x)=(sinx,1).(2cosx-sinx,-1/2-1)=2sinxcosx-(sinx)^2-3/2=sin2x-(sinx)^2-3/2
f'(x)=2cos2x-2sinxcos=2(cos2x-sin2x)=2√2sin(2x-π/4)≥0
2kπ-π/2≤2x-π/4≤2kπ+π/2
kπ-π/8≤x≤kπ+3π/8 (k为整数)
f(x)=2ab-a²+cos²x=2(sinxcosx-1/2)+(cos2x+1)/2=sin2x+cos2x-1/2
=根号下2sin(2x+π/4)-1/2
单调增区间为：2kπ-π/2≤2x+π/4≤2kπ+π/2
kπ-3π/8≤x≤kπ+π/8
即增区间为[kπ-3π/8,kπ+π/8].
f(x)=2ab-a²+cos²x
=根号下2sin(2x+π/4)-1/2
调增区间为：2kπ-π/2≤2x+π/4≤2kπ+π/2
kπ-3π/8≤x≤kπ+π/8
即增区间为[kπ-3π/8,kπ+π/8]