y= sin(t)的单调区间
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设t=2x-π/3
y=sint的对称轴是t=kπ+π/2,k∈z,单调增区间是[2kπ-π/2,2kπ+π/2],k∈z,单调减区间是[2kπ+π/2,2kπ+3π/2],k∈z
对于y=sin(2x-∏/3),由2x-π/3=kπ+π/2,k∈z,得到x=kπ/2+5π/12,k∈z,
即对称轴是,x=kπ/2+5π/12,k∈z
又由2kπ-π/2<=2x-π/3<=2kπ+π/2,kπ-π/12<=x<=kπ+5π/12
所以 单调增区间是[kπ-π/12,kπ+5π/12],k∈z
同样2kπ+π/2<=2x-π/3<=2kπ+3π/2,kπ+5π/12<=x<=kπ+11π/12
所以单调减区间是[kπ+5π/12,kπ+11π/12]k∈z
y=sint的对称轴是t=kπ+π/2,k∈z,单调增区间是[2kπ-π/2,2kπ+π/2],k∈z,单调减区间是[2kπ+π/2,2kπ+3π/2],k∈z
对于y=sin(2x-∏/3),由2x-π/3=kπ+π/2,k∈z,得到x=kπ/2+5π/12,k∈z,
即对称轴是,x=kπ/2+5π/12,k∈z
又由2kπ-π/2<=2x-π/3<=2kπ+π/2,kπ-π/12<=x<=kπ+5π/12
所以 单调增区间是[kπ-π/12,kπ+5π/12],k∈z
同样2kπ+π/2<=2x-π/3<=2kπ+3π/2,kπ+5π/12<=x<=kπ+11π/12
所以单调减区间是[kπ+5π/12,kπ+11π/12]k∈z
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