Question

函数y=2sin(π/3-2x)的单调减区间是______

Answer 1

因为y=sinx的单调减区间为
[π/2+2kπ,3π/2+2kπ],k为任意整数，
所以函数y=2sin(π/3-2x)的单调减区间
为
π/2+2kπ<=π/3-2x<=3π/2+2kπ
π/6+2kπ<=-2x<=7π/6+2kπ
π/12+kπ<=-x<=7π/12+kπ
-7π/12-kπ<=x<=-π/12-kπ
即单调减区间为
[-7π/12-kπ,-π/12-kπ],k为任意整数。

Answer 2

y=-sin(2x-π/3)
所以y和sin(2x-π/3)单调性相反
所以y减区间即sin(2x-π/3)的增区间
sinx的增区间是(2kπ-π/2,2kπ+π/2)
所以2kπ-π/22kπ-π/6kπ-π/12所以y的减区间是(kπ-π/12,kπ+5π/12)

Answer 3

y=2sin(π/3-2x)=-2sin(2x-π/3)
要求函数y的单调减区间，即求y=2sin(2x-π/3)的单调增区间
函数y=sinx的单调增区间是π/2+2kπ

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