The monotone decreasing interval of the function y = sin (x + 4 / π) is a monotone increasing interval

The monotone decreasing interval of the function y = sin (x + 4 / π) is a monotone increasing interval

X + 4 / π∈ [- π / 2 + 2K π, π / 2 + 2K π] increasing interval
The increasing interval of X ∈ [- 3 π / 4 + 2K π, π / 4 + 2K π] is obtained
X + 4 / π∈ [π / 2 + 2K π, 3 π / 2 + 2K π] minus interval
X ∈ [π / 4 + 2K π, 5 π / 4 + 2K π] minus interval is obtained

Find the equation of the least positive period and symmetry axis of F (x) = sin (2x + π / 6)

The minimum positive period of F (x) = sin (2x + Pai / 6) t = 2pai / 2 = Pai
The equation of symmetry axis is 2x + Pai / 6 = KPAI + Pai / 2
That is, x=kPai/2+Pai/6

The minimum positive period and symmetric axis equation of F (x) =sin (2x+1/6 π) +2sin^2x

f(x)=sin(2x+1/6π)+2sin^2x
=sin(2x+1/6π)+1-cos2x
=(√3sin2x)/2+(cos2x)/2+1-cos2x
=sin(2x-π/6)+1
The minimum positive period is π
The equation of symmetry axis is x = k π / 2 + π / 3

F (x) = sin (2x + 30 °) to find the minimum positive period and symmetric axis equation!

Minimum positive period T = 2 π / 2 = π
The symmetry axis equation 2x + π / 6 = k π + π / 2, K belongs to Z
That is, the symmetric axis equation x = k π / 2 + π / 6, K belongs to Z

F (x) = cos? X + 2sinxcosx-sin? X to find the period, the increasing interval and the axis of symmetry Let's move in

f(x)=cos²+2sinxcosx-sin²x
=cos2x+sin2x
=2Sin (2x + π / 4) under radical
Period = 2K π / 2 = k π
2kπ-π/2

Find the symmetry center of the function y = 3-2cos (2x - π / 3), the equation of symmetry axis, and when x is the value, y gets the maximum or minimum value

2X - π / 3 = k π + π / 2, x = k π / 2 + 5 π / 12 symmetry center (K π / 2 + 5 π / 12,0)
2X - π / 3 = k π, symmetry axis equation x = k π / 2 + π / 6,
When 2x - π / 3 = 2K π, x = k π + π / 6, y min = 1
When 2x - π / 3 = 2K π + π, x = k π + 2 π / 3, y max = 5

F (x) = 4sinx * sin (x + Pai / 3)

f(x)=4sinx*sin(x+pai/3)=4sinx*(1/2 sinx+3^(1/2)/2 cosx)=2(sinx)^2+2*3^(1/2) sinxcosx=2-2(cosx)^2+3^(1/2) sin2x=1-cos2x+3^(1/2) sin2x=1-2(0.5cos2x-0.5*3^(1/2) sin2x)=1-2cos(2x+pai/3)
To find the monotone increasing interval of F (x) is actually to find the monotone decreasing interval of COS (2x + Pai / 3)
Then 2kpai

0

y=sin(pi/4-x)
Let t = pi / 4-x
Then: y = sin (T)
Then y = the monotone increasing interval of sin (T)
2kpi-pi/2

F (x) = - 1 / 2 + sin (PAI / 6-2x) + cos (2x Pai / 3) + cos ^ 2x to find the minimum positive period of F (x)

f(x)=-1/2+1/2cos2x-√3/2sin2x+1/2cos2x+√3/2sin2x+cos^2x=-1/2+cos2x+cos^2x=-1/2+cos^2x-sin^2x+cos^2x=-3/2+3cos^2x=-3/2+3(1+cos2x)/2=-3/2+3/2+3/2cos2x=3/2cos2xT=2pi/2=pi

Try to find the monotone interval of the function f (x) = log2 (x ^ 2-2x-3)

Because 2 > 1, the original function is a monotone increasing function,
Because x ^ 2-2x-3 > 0,
(x-3)(x+1)>0,
So x > 3 or X3 or X