The function y = cos (2x + π) 4) The monotone decreasing interval of is______ .

The function y = cos (2x + π) 4) The monotone decreasing interval of is______ .

From 2K π ≤ 2x + π
4≤2kπ+π，
That is k π - π
8≤x≤kπ+3π
8，k∈Z
So the monotone decreasing interval of the function is [K π − π
8，kπ+3π
8](k∈Z)，
So the answer is: [K π - π
8，kπ+3π
8](k∈Z)．

The monotone increasing interval of the function f (x) = cos (13 / 2 pai-2x) is

f(x)=cos(13/2π-2x) =cos(6π+π/2 -2x)
= cos(π/2 -2x)=sin(2x),
2kπ-π/2≤2x≤2kπ+π/2,
kπ-π/4≤x≤kπ+π/4.(k∈Z)
So the increasing interval of the function is [K π - π / 4, K π + π / 4] (K ∈ z)

A monotone increasing interval of the function y = sin (x-pai / 3) is A.（-pai/6,5pai/6） B.（-5pai/6,pai/6） C.（-pai/2,pai/2） D.（-pai/3,2pai/3）

The increasing range of y = SiNx is (- Pai / 2 + 2kpai, Pai / 2 + 2kpai)
Y = sin (x-pai / 3) is to translate y = SiNx to the right Pai / 3 units
So the monotone Zeng interval shifts Pai / 3 units to the right
（-pai/6+2kpai,5pai/6+2kpai)
A

The function f (x) = sin (x + π) 4) In the following intervals, the monotonically increasing interval is () A. [π 2，π] B. [0，π 4] C. [-π，0] D. [π 4，π 2]

When x ∈ [0, π
4] X + π
4∈[π
4，π
2] So the function f (x) = sin (x + π)
4) At [0, π
4] It's an increasing function,
So [0, π
4] Is the function f (x) = sin (x + π)
4) A monotonically increasing interval of,
Therefore, B

Find the monotone increasing interval of function y = sin (1 / 2x + Pai / 3) and find the great solution

2kπ-π/2≤1/2x+π/3≤2kπ+π/2
2kπ-5π/6≤1/2x≤2kπ+π/6
4kπ-5π/3≤x≤4kπ+π/3
Namely
The monotone increasing interval is: [4K π - 5 π / 3,4k π + π / 3], K ∈ Z

Let f (x) = sin (2x + Pai / 6) be used to solve the equations of the least positive period and symmetric axis

If the minimum positive period T = 2 π / ω = 2 π / 2 = π, let 2x + π / 6 = t, then the original function becomes y = Sint, its symmetry axis is t = k π + π / 2, and then let 2x + π / 6 = k π + π / 2, x = k π / 2 + π / 6 can be obtained, which is the axis of symmetry

The period, monotone interval, maximum value and symmetry axis of y = sin (2x + π / 6) + cos 2 X-1

y=sin(2x+π/6)+cos²x-1=sin2xcos(π/6)+cos2xsin(π/6)+(1/2)cos2x-(1/2)=(√3/2)sin2x+cos2x-(1/2)=(√7/2)*[(√3/√7)sin2x+(2/√7)cos2x]-(1/2)=(√7/2)sin(2x+φ)-(1/2)…… Zero

1. Y = 2 sin (2x + π / 4) + 22. Y = 2cos (π / 4-2x)

1. So, let's say that we can get 2 × 2 + 2 + 2 + 2,
So we know: - π / 2 + 2K π

F (x) = LG [sin (PAI / 3-2x)] monotonically increasing interval

Since the base number of LG is greater than 1, only its definition field is required

The minimum positive period of F (x) = cos (x + Pai / 3) + sin ^ 2x?

The minimum positive period of COS (x + π / 3) is 2 π
Sin ^ 2x = (1-cos2x) / 2 minimum positive period: π
So the minimum positive period of F (x): 2 π