F (x) = (1 + cos2x) sin ^ 3x to find out whether the minimum positive period of a function is odd or even,

F (x) = (1 + cos2x) sin ^ 3x to find out whether the minimum positive period of a function is odd or even,

f(x)=(1+cos2x)sin^3x=2cosxcosxsinxsinxsinx=1/2sin2x sinx
f（-x）=1/2sin（-2x）sin（-x）=1/2sin2x sinx=f（x）
So f (x) is even function
The period of SiNx is 2 π, and the period of sin2x is t = π
Therefore, the period of F (x) is the larger one, t = π
It is proved that f (x + 2 π) = 1 / 2Sin (2x + 2 π) sin (x + π) = 1 / 2sin2x SiNx = f (x)
So t = 2 π

The function y = sin2x + cos2x is () A. Even functions with period π B. Odd functions with period π C. Increasing function with period 2 π D. Subtraction function with period 2 π

Y=1
2（1-cos2x）+cos2x=1
2cos2x+1
2，
∵ω=2，∴T=π，
∵ cosine function is even function,
The function y is an even function with period π
So choose a

Is y = SiNx (cosx) odd or even In the middle of SiNx and cosx is multiplication

Method 1: F (x) = (SiNx) (cosx) f (- x) = sin (- x) * cos (- x) = - SiNx * cosx = - f (x), odd function method 2: F (x) = (SiNx) (cosx) = 0.5sin (2x) f (- x) = 0.5sin (- 2x) = - 0.5sin (2x) = - f (x), odd function

Is y = ︱ SiNx + 3 an odd function or even function But isn't sine function odd? Isn't sin (- x) equal to - SiNx, that is, to compare with absolute value, is it?

Y = ︱ SiNx + 3 is even function
Because first of all, X belongs to the domain symmetry of real number definition
Second: when x takes - X
y=｜sin-x｜+3 =｜sinx｜+3
According to f (x) = f (- x), we get that y = ︱ SiNx + 3 is even function
Where not clear send a message to ask me, I am online

It is known that the quadratic function f (x) is an even function, and its analytic formula is obtained through the point (3,6)

Quadratic function f (x) is even function
∴f(x)=ax^2+c
I didn't say yesterday that even functions have coefficients of odd powers of 0
Passing point (3,6)
Substitution
9a+c=6
c=6-9a
∴y=ax^2+6-9a
Only one relation can be obtained

The function f (x) is an even function whose period is the one in two. If f (the third part) is equal to 1, find f (- 17 of 6)

T=π/2
f(-17π/6)
=f(-π/3-7×π/2)
=f(-π/3)
Even function
=f(π/3)
=1

If the function f (x) is an even function with period π / 2 and f (π / 3) = 1, find the value of F (- 17 / 6 * π),

f(-17π/6)=f(-3π+π/6)=f(π/6)=f(-π/3)=f(π/3)=1

When x belongs to [2,4], f (x) = 4-x, then f (- 7.4)= Detailed problem solving steps, with text description

f(x+4)=f(x)
f(-3.4)=f(-7.4)
It's even,
f(3.4)=0.6
f(-3.4)=0.6
f(-7.4)=0.6

It is known that the function f (x) is an even function defined on R, and when x is less than or equal to 0, f (x) = x square + 2x 1: Write the value range of the function f (x) (x belongs to R) 2: Write the analytic expression of the function f (x) (x belongs to R)

Even function description about Y-axis symmetry
f(x)=x^2+2x=(x+1)^2-1
The range of values is that f (x) is greater than or equal to - 1
Analytic formula
When x is less than or equal to 0, f (x) = x ^ 2 + 2x
When x is greater than 0, f (x) = x ^ 2-2x

It is known that the quadratic function f (x) is an even function and an analytic expression of it is obtained through the point (3,6)

y=(2/3)x^2