求函数Y=1/2sin(π/4-2/3X)的单调区间

题目

求函数Y=1/2sin(π/4-2/3X)的单调区间
如题

答案

y=-1/2sin(2/3x-π/4)
所以y和sin(2/3x-π/4)单调性相反
sinx的增区间是(2kπ-π/2,2kπ+π/2)
减区间是(2kπ+π/2,2kπ+3π/2)
所以sin(2/3x-π/4)单调增时
2kπ-π/2<2/3x-π/4<2kπ+π/2
2kπ-π/4<2/3x<2kπ+3π/4
3kπ-3π/8同理,单调减时是3kπ+9π/8y和sin(2/3x-π/4)单调性相反
所以
增区间(3kπ+9π/8,3kπ+21π/8)
减区间(3kπ-3π/8,3kπ+9π/8)