If the function f (x) = sin ω x (ω > 0) increases monotonically in the interval [0, π 3] and decreases monotonically in the interval [π 3, π 2], then ω = () A. 23B. 32C. 2D. 3

If the function f (x) = sin ω x (ω > 0) increases monotonically in the interval [0, π 3] and decreases monotonically in the interval [π 3, π 2], then ω = () A. 23B. 32C. 2D. 3

It can be seen from the meaning that the maximum value of the function is determined when x = π 3, that is, ω π 3 = 2K π + π 2, K ∈ Z, so ω = 6K + 32; only when k = 0, ω = 32 satisfies the option

The monotone decreasing interval of the function y = sin (π / 3-x) is

Correlation method
The monotonic subtraction of SiNx is [2kpi + pi / 2,2kpi + 3pi / 2]
So pi / 3-x should belong to [2kpi + pi / 2,2kpi + 3pi / 2]
2kpi+pi/2=

The monotone decreasing interval of the function y = sin (π 4 − x) in the interval [0,2 π] is ()
A. [π4，5π4]B. [3π4，7π4]C. [0，π4]，[5π4，2π]D. [0，3π4]，[7π4，2π]

The function y = sin (π 4 − x) is reduced to: y = − sin (x − π 4), because x − π 4 ∈ [2K π − π 2, 2K π + π 2] & nbsp; & nbsp; K ∈ Z, so x ∈ [2K π − π 4, 2K π + 3 π 4] & nbsp; & nbsp; K ∈ Z, the monotone decreasing interval of function y = sin (π 4 − x) in the interval [0, 2 π] is: [0, 3 π 4], [7 π 4, 2 π]. So D is selected