It is known that the minimum value of the function f (x) = - Cos2 ^ 2x-2asinx + 6 (x belongs to R) is 2,

It is known that the minimum value of the function f (x) = - Cos2 ^ 2x-2asinx + 6 (x belongs to R) is 2,

The original formula is y = cosx asinx-a 2A 5 = 1-sinx asinx-a 2A 5 = - (sinx-a / 2) - 3A / 4 2A 6. If sinx-a / 2 = 0, then - 3A / 4 2A 6 = 2, that is, 3a-8a-16 = 0 (3a 4) (A-4) = 0, then a = - 4 / 3 or a = 4

The maximum and minimum of y = cosx + 1 and the corresponding x set

∵ cos α ranges from - 1 to 1
The maximum and minimum values of Y are 2 and 0, respectively
The set is 2K π and 2K π + π, respectively

When the function y = cosx / 3 takes the maximum value, the value set of the independent variable x is

∵ when t = 2K π, K ∈ Z, the maximum value of y = cost is 1
When x / 3 = 2K π, K ∈ Z, the function y = cosx / 3 gets the maximum
That is, when x = 6K π, K ∈ Z, the function y = cosx / 3 gets the maximum
The set of values of X is {x | x = 6K π, K ∈ Z}

Given the function y = 1 / 2cosx * cosx + √ 3 / 2sinx * cosx + 1. When the function y reaches the maximum, find the set of independent variables X
How to translate and shrink the image of y = SiNx?

y=1/2cosx*cosx+√3/2sinx*cosx+1
=1/4(2(cosx)^2-1+√3*2sinx*cosx)+5/4
=1/2(1/2*cos2x+√3/2*sin2x)+5/4
=1/2*sin(2x+π/6)+5/4
When y is the maximum, sin (2x + π / 6) = 1
That is, 2x + π / 6 = 2K π + π / 2
x=kπ+π/6 (k ∈ Z)
y=1/2*sin(2x+π/6)+5/4
=1/2*sin(2(x+π/12))+5/4
The graph y = SiNx moves π / 12 to the left in the horizontal direction, shrinks to 1 / 2 of the original, shrinks to 1 / 2 of the original in the vertical direction, and moves up 5 / 4

The maximum value of y = 2sinx + cosx is

Root 5

The maximum value of the function y = 2sinx cosx is______ ．

Y = 2sinx cosx = 5sin (x + φ) ≤ 5, so the answer is: 5

Given the function y = 3sin (2x + π / 3), if the function y = 3sin (2x + π / 3) + B has the maximum value 2, find the minimum value of the value function of B

y=3sin(2x+π/3）,
-3

Find the set of maximum, minimum and corresponding x values of the following functions y = 3sin (3x / 4 - π / 4)
Speed, detailed process, see the problem

The sin range is [- 1,1]
So the maximum values of Y are - 3 and 3
sin(3x/4-π/4)=1
3x/4-π/4=2kπ+π/2
3x/4=2kπ+3π/4
x=8kπ/3+π
In the same way
sin(3x/4-π/4)=-1
3x/4-π/4=2kπ-π/2
x=8kπ/3-π/3
X ∈ {x | x = 8K π / 3 + π, K ∈ Z}, y max = 3
X ∈ {x | x = 8K π / 3 - π / 3, K ∈ Z}, y min = - 3

The maximum value of the function y = 2 + 3sin (2 / x) is_____ In this case, the set of X is____ The minimum value is_____

The maximum value is 5, then the set of X is 4 / [(2k + 1) * PI], K is any integer, and the minimum value is - 1

Mathematical problems solved by equations
The export output value of a factory in May this year is 2.4 million, which is 1 / 10 lower than that of the same period last year

1. Let x years later, the father's age is exactly five times the son's age. Son this year: 32 △ 4 = 8 (years old) 32 + x = 5 (8 + x) 32 + x = 40 + 5x 4x = 8 x = 2 A: two years later, the father's age is exactly five times the son's age. Uncle Wang is x years old, while Xiaoying is x-8-8 = x-16 (years old)