y=cos(2x+π/3),x∈[-2π,2π]的单调递增区间
y=cos(2x+π/3),则周期T=π
设2x+π/3=X,则X∈[-11π/3,13π/3]
由cosX单调递增区间为[π加减2kπ,2π加减2kπ]可得在X∈[-11π/3,13π/3]区间上的递增区间为
X=2x+π/3∈[π加减2kπ,2π加减2kπ],k=-2,-1,0,1
换算后可得y的递增区间
x∈[π/3加减kπ,5π/6加减kπ],k=-2,-1,0,1
应该够详细了
y=cos(2x+π/3),x∈[-2π,2π]的单调递增区间
y=cos(2x+π/3),则周期T=π
设2x+π/3=X,则X∈[-11π/3,13π/3]
由cosX单调递增区间为[π加减2kπ,2π加减2kπ]可得在X∈[-11π/3,13π/3]区间上的递增区间为
X=2x+π/3∈[π加减2kπ,2π加减2kπ],k=-2,-1,0,1
换算后可得y的递增区间
x∈[π/3加减kπ,5π/6加减kπ],k=-2,-1,0,1
应该够详细了