What is the maximum value of the function y = sin? X-cos? X + 2cosx-2?

What is the maximum value of the function y = sin? X-cos? X + 2cosx-2?

y=1-cos²x-cos²x+2cosx-2=-2cos²x+2cosx-1=-2（cosx-1/2）²-1+1/2=-2（cosx-1/2）²-1/2

The function f (x) = sin2x + 2cosx in the interval [- 2] If the maximum value of 3 π, θ] is 1, then the value of θ is () A. 0 B. π Three C. π Two D. -π Two

∵f（x）=sin2x+2cosx=-cos2x+2cosx+1=-（cosx-1）2+2，
In the interval [- 2 π
The maximum value of 3, θ] is 1
Combined with the options, we can see that θ can only take - π
2．
Therefore, D is selected

Given the function f (x) = 2cosx (SiNx cosx), X ∈ R, (1) find the minimum and maximum value of function f (x) on the interval [π / 8,3 π / 4]

f(x)=2sinxcosx-2(cosx)^2
=sin2x-(1+cos2x)
=sin2x-cos2x-1
=√2sin(2x-π/4)-1
π/8≤x≤3π/4
π/4≤2x≤3π/2
0≤2x-π/4≤5π/4
The minimum value of [sin / 2] is π / 2
-√2/2≤sin(2x-π/4)≤1
-1≤√2sin(2x-π/4)≤√2
-2≤√2sin(2x-π/4)-1≤√2-1
So,
f(max)=√2-1
f(min)=-2

Find the maximum and minimum of the function y = (1-sinx) / (3 + 2cosx)

y = (1-sinx)/(2cosx+3) ≥ 0 ∵1-sinx = 2ycosx+3y 2ycosx+sinx = 1-3y √[(2y)²+1] sin(x+T) = 1-3y .tanT=2y 1-3y≤√[(2y)²+1] 1-6y+9y²≤4y²+1 ∴5y²-6y=y(5y-6)≤0 ∴ 0≤y≤6/5...

The minimum positive period of the function f (x) = (1 + cos2x) sin? X (x belongs to R) is?

f(x)=(1+cos2x)sin²x=(1+2cos²x-1)sin²x=2cos²xsin²x=1/2sin²2x
The minimum positive period is t = 2 π / 4 = π / 2

F (x) = (1 + cos2x) sin? X, X ∈ R, and find the minimum positive period and parity of the function Explain

f(x)=2cos^2x*sin^2x=1/2(sin2x)^2=(1-cos4x)/4
T=2π/w=π/2
f(-x)=(1-cos(-4x))/4=f(x)
The minimum period of F (x) is π / 2

The minimum positive period of the function y = sin? X is

y=sin²x
=(1-cos2x)/2;
=1/2-cos(2x)/2;
The minimum positive period = 2 π / 2 = π;
If there is anything you don't understand, you can ask,

The minimum positive period of the function y = sin2x is______ .

The minimum positive period of the function y = sin2x is 2 π
2=π，
So the answer is: π

Find the period of the function y = sin? X,

dawn
Whether I'm standing on a driveway or a gray sidewalk,
Love years ago,
It also annoys some people
The air is full of air from another world
The face is as like as two peas.

Find the value range of the function f (x) = sin? X + cosx-3 / 2

Let t = cosx, then | t|