已知函数f(x)=cosx-cos(x+π/2) x∈R(1)求f(x)的最大值和最小值(2)求f(x)的单调递增区间已知函数f(x)=cosx-cos(x+π/2) x∈R(1)求f(x)的最大值和最小值(2)求f(x)的单调递增区间
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已知函数f(x)=cosx-cos(x+π/2) x∈R(1)求f(x)的最大值和最小值(2)求f(x)的单调递增区间已知函数f(x)=cosx-cos(x+π/2) x∈R(1)求f(x)的最大值和最小值(2)求f(x)的单调递增区间
已知函数f(x)=cosx-cos(x+π/2) x∈R(1)求f(x)的最大值和最小值(2)求f(x)的单调递增区间
已知函数f(x)=cosx-cos(x+π/2) x∈R
(1)求f(x)的最大值和最小值
(2)求f(x)的单调递增区间
已知函数f(x)=cosx-cos(x+π/2) x∈R(1)求f(x)的最大值和最小值(2)求f(x)的单调递增区间已知函数f(x)=cosx-cos(x+π/2) x∈R(1)求f(x)的最大值和最小值(2)求f(x)的单调递增区间
f(x)=cosx-cos(x+π/2)
=-2(sin(x+x+π/2)/2sin(x-x-π/2)/2
=-2(sin(x+π/4)sin(-π/4)
=√2sin(x+π/4)
所以最大值是√2,最小值是-√2
增区间 2kπ+π/2>=x+π/4>=2kπ-π/2
2kπ+π4>=x>=2kπ-3π/4区间为增区间
减区间 2kπ+3π/2>=x+π/4>=2kπ+π/2
2kπ+5π/4>=x>=2kπ+π/4区间为减区间
f(x)=cosx-cos(x+pi/2)=cosx+sinx=根号下2 *(sin45cosx+cos45sinx)=根号2 sin(pi/4+x)
max=根号2
min=-根号2
增区间为(-3pi/4+2kpi,pi/4+2kpi)
减区间为(pi/4+2kpi,5pi/4+2kpi) k为整数
f(x)=cosx-cos(x+π/2)
=-2(sin(x+x+π/2)/2sin(x-x-π/2)/2
=-2(sin(x+π/4)sin(-π/4)
=√2sin(x+π/4)
所以max是√2min是-√2
增区间[2kπ-3π4,2kπ+π/4]
减区间[2kπ+4π/4,2kπ+5π/4]