Is y = | SiNx | a periodic function By the way, is y = | tanx| a periodic function? If so, what is the period?

Is y = | SiNx | a periodic function By the way, is y = | tanx| a periodic function? If so, what is the period?

Y = | SiNx | is a periodic function, t = π
Y = | TaNx | is also a periodic function, t = π

Find the value range of the function: (1) y = | SiNx | - 2sinx (2) y = sin | x | SiNx|

(1) The value range is [- 1,3] and can be drawn or classified for discussion
(2) This is even function
So about the y-axis symmetry
When x > = 0, y = sinx|sinx|
The range is [- 1,1]

What is the primitive function of sin ^ 2x? What is the primitive function of the square of SiNx? Derivative`

Half x minus half the cos2x

Given the function y = sin 2 x - (1 / 2) SiNx + 1 (x ∈ R), if x = α when y is the maximum and x = β when y is the minimum, and α, β∈ [- π / 2, π / 2] then sin (α + β)=

First, we get y = (sinx-1 / 4) ^ 2 + 15 / 16, because when x ∈ R, SiNx = 1 / 4 has a solution, so the minimum value is taken at SiNx = 1 / 4, that is, sin β = 1 / 4; for the maximum value, because the value range of SiNx is [- 1,1]
So when SiNx = - 1, y reaches the maximum value, i.e. sin α = - 1, α = - π / 2=
Sin (- π / 2 + β) = - cos β, from β∈ [- π / 2, π / 2], and sin β = 1 / 4, cos β = 15 / 4,
So sin (α + β) = - radical 15 / 4

If f (x) = (1 + cos2x) sin ^ 2 (x), X belongs to R, then f (x) period? Odd even?

The original formula = [sin ^ 2 (x) + cos ^ 2 (x) + cos ^ 2 (x) - Sin ^ 2 (x)]
=2cos^2(x)sin^2(x)=1/2sin^2(2x)
So the period is π, even

Find the minimum positive period of the function y = (SiNx + cosx) 2 + 2cos2x=______ .

y=1+sin 2x+2cos2x=sin 2x+cos 2x+2
=
2 (
Two
2sin2x+
Two
2cos2x)+2
=
2sin（2x+π
4）+2．
So the minimum positive period is 2 π
2=π．
So the answer is: π

The function f (x) = (1 + cos2x) sin ^ 2x is the function with period (odd,

f(x)=(1+2cos^2x-1)sin^2x=2cos^2x*sin^2x=1/2sin^2(2x)=1/4（1-cos4x)
So its period is pi / 2

If f (x) = (1 + cos2x) sin ^ 2x, X belongs to R, then the minimum positive period of F (x) is

f(x)=(1+cos2x)sin^2x=2cosx^2sinx^2=1/2(sin2x)^2
The minimum period is pie

Is the function y = sin square x periodic and parity?

f(x)=sin²x
=(1-cos(2x))/2
Period T = 2 π / 2 = π
f(-x)
=(1-cos(-2x))/2
=(1-cos(2x))/2
=f(x)
It's even function

It is proved that y = sin (the square of x) is not a periodic function Attention Oh, it's "no", so don't say math food

Suppose the periodic function y (x + T) = y (x)
sin[(x+T)^2]=sin(x^2)
Then (x + T) ^ 2 = x ^ 2 + 2K π or (x + T) ^ 2 = π - x ^ 2 + 2K π K is an integer
(x + T) ^ 2 = x ^ 2 + 2K π = > 2tx + T ^ 2 = 2K π holds for all x, only t = k = 0
The latter gives t = 0, k = 1 / 2 (omitted)
In short, the period T = 0
So it's not a periodic function