Is the periodic sum of y = sin (x + 3 π / 4) + cos (x + 3 π /) odd or even?

Is the periodic sum of y = sin (x + 3 π / 4) + cos (x + 3 π /) odd or even?

Is it y = sin (x + 3 π / 4) + cos (x + 3 π / 4)?
y=√2sin(x+3π/4+π/4)=√2sin(x+π)=-√2sinx
Period 2 π, odd function

Is y = sin (PAI / 4 + x) cos (PAI / 4 + x) odd or even? What is the period?

y=1/2*[2sin(π/4+x)cos(π/4+x)]
=1/2*sin[2(π/4+x)]
=1/2*sin(π/2+2x)
=1/2*cos2x
So this is even function
T=2π/2=π

Find the period of the function y = sin ^ 3 (x) + cos ^ 3 (x),

The period of F (x) = sin 3 x is 2 π, and that of G (x) = cos 3 x is 2 π
So the period of y = sin 3 x + cos 3 x is also 2 π

The minimum positive period of the function y = (COS ^ 2x sin ^ 2x) * tan2x is

Y = (COS ^ 2x sin ^ 2x) * tan2x = cos2xtan2x = sin2x, isn't the period Pi?

Is the minimum positive period of the function y = cos ^ 2x sin ^ 2x?

y=cos^2x-sin^2x
=cos2x
Minimum positive period = 2 * pi / 2 = Pi

The minimum positive period of the function y = sin (2x + Pai / 6) cos (2x + Pai / 6) is

Using the double angle formula sin2x = 2sinx * cosx, we can get y = sin (2x - π / 6) * cos (2x - π / 6) = 0.5sin (4x - π / 3) because the minimum positive period of y = asin (AX + b) is 2 π / A, so the minimum positive period of this function is 2 π / 4 = π / 2

The minimum positive period of the function y = sin π x * cos π x is thank

The minimum positive period of the function y = sin π x * cos π x is
y=sinπxcosπx=(1/2)sin(2πx)
Therefore, the minimum positive period Tmin = 2 π / 2 π = 1

Function y = 1 + SiNx The value range of 2 + cosx is () A. [-4 3，4 3] B. [-4 3，0] C. [0，4 3] D. （0，4 3]

∵y=1+sinx
2+cosx，
∴1+sinx=2y+ycosx，
∴sinx-ycosx=2y-1，
Namely:
1+y2sin（x-θ）=2y-1，
∵-
1+y2≤
1+y2sin（x-θ）≤
1+y2，
∴-
1+y2≤2y-1≤
1+y2，
The solution is: y ∈ [0,4]
3]．
Therefore, C

Find the value range of function y = cos + 2 / SIN-1

Y = (cosx + 2) / (sinx-1) ysinx-y = cosx + 2ysinx-cosx = y + 2 √ (y? 2 + 1) sin (x-t) = y + 2, t = arctan (1 / y) sin (x-t) = (y + 2) / √ (y? + 1), so | y + 2 | / √ (Y | 1) ≤ 1y | + 4Y + 4 ≤ y ≤ - 3 / 4

The value range of the function y = sin α / │ sin α │ + CoS / │ cos α │ is The process! Thank you y=sinα/│sinα│+cosα/│cosα│ Do you want the process... [why]?

The range of the angle to be considered is as follows:
When a is in the first quadrant, Sina > 0, cosa > 0, y = 2
When a is in the second image limit, Sina > 0, cosa