周期:函数y=sin(x+3.14/3)sin(x+3.14/2)的最小正周期T=

问题描述:

周期:函数y=sin(x+3.14/3)sin(x+3.14/2)的最小正周期T=
文科班小尤提问啦:
函数y=sin(x+3.14/3)sin(x+3.14/2)的最小正周期T=
第一名,看清楚题目好不好!一个是除2,一个是除3

y=sin(x+π/2)sin(x+π/3)
=-[cos(x+π/2+x+π/3)-cos(x+π/2-x-π/3)]/2
=-[cos(2x+5π6)-cosπ/6]/2
=-(1/2)cos(2x+5π6)+√3/4
所以T=2π/2=π