Find the minimum positive period of F (x) = SiNx / 2 quartic power + cosx / 2 quartic power + quarter root sign three times sin2x

Find the minimum positive period of F (x) = SiNx / 2 quartic power + cosx / 2 quartic power + quarter root sign three times sin2x

=(（sin^2 (x/2) +(cos^2 (x/2))^2-2×sin^2(x/2)cos^2(x/2)+ √3/4sin2x=1-1/2(2sin(x/2)con(x/2))^2+√3/4sin2x=1-1/2sin^2(x)+ √3/4sin2x=1-1/2(1/2×(1-cos2x))+√3/4sin2x=1-1/4+1/4cos2x+√3/4sin2x=3/4+1/2(...

The maximum value of the function y = 7 / 4 + SiNx - (SiNx) ^ 2 is
..

The maximum value of function y = 7 / 4 + SiNx - (SiNx) ^ 2, y = - [(SiNx) ^ 2-sinx-7 / 4] = - [(sinx-1 / 2) ^ 2-1 / 4-7 / 4] = - (sinx-1 / 2) ^ 2 + 2, because the minimum value of (sinx-1 / 2) ^ 2 is 0, the maximum value of y = - (sinx-1 / 2) ^ 2 + 2 is 2

What is the maximum value of the function y = 2 / SiNx + SiNx / 2 (0 < x ≤ π / 2)
What is the abscissa of the point on the parabola y ^ 2 = - 4x at a distance of 4 from the focus

1
No maximum value:
When x → 0, SiNx → 0;
Then 2 / SiNx → + ∞
two
According to the definition of parabola, the distance from a point on the parabola to the focus is equal to the distance from the parabola to the collimator
The guide line is x = - 1,
Then: - 1-x0 = 4
→ x0=-5.

If y = x-sinx, then when x ∈ [0, π], the maximum value of the function is

y=x－sinx
Then:
y'=1－cosx>0
Then the function increases in the interval [0, π], and the maximum value of the function is f (π) = π