Given the function f (x) = sin (2x + 6 / π) + sin (2x-6 / π) (a is a constant) (1), find the minimum of the function Given the function f (x) = sin (2x + 6 / π) + sin (2x-6 / π) (a is a constant) (1) find the minimum positive period of the function, monotone decreasing interval (2) if x ∈ [0,2 / π], the minimum value of F (x) is - 2, find the value of A

Given the function f (x) = sin (2x + 6 / π) + sin (2x-6 / π) (a is a constant) (1), find the minimum of the function Given the function f (x) = sin (2x + 6 / π) + sin (2x-6 / π) (a is a constant) (1) find the minimum positive period of the function, monotone decreasing interval (2) if x ∈ [0,2 / π], the minimum value of F (x) is - 2, find the value of A

f(x)=sin(2x+6/π)+sin(2x-6/π)
=√3/2sin2x+1/2cos2x+√3/2sin2x-1/2cos2x
=√3sin2x
T=2π/2=π
2X is monotonically decreasing in [2K π + π / 2,2k π + 3 π / 2]
X is monotonically decreasing in [K π + π / 4, K π + 3 π / 4]
2)
3 points for 1 grain, 4 points for 1 grain, 1 point for 12 grains, 100 points for each grain (this is a math problem)
I calculated,
Let three parts of X, four parts of Y, one part of Z,
3x+4y+1/12 z=100
x+y+z=100
Finally, we got
x=18,Y=10,Z=72
The proof of the period of function
Y = sinxsinx; y = xcosx; are these two functions periodic? If so, what is the period? If not, how to prove it?
The first one is solved by the above two figures
Second, suppose it's a periodic function
Let the period be K
xcosx=（x-k)cos(x-k)
=(x-k)(cosxcosk+sinxsink)
=xcoxcosk+xsinxsink-kcos(x-k)
At this time, you can see that if you want them to be equal, K must be equal to 0, and a function with a period of 0 cannot be called a periodic function
The first is that the square of sin is equal to (1-cos2x) / 2, and the period is pi
The second is not
Y = sinxsinx = (1-cos2x) / 2, because cosx is a periodic function with period of 2 π, its period is 2 π / 2 = π
y=sinxsinx=sin^2x=(1-cos2x)/2
So the minimum positive period is pi
Y = xcosx has no period
12+56+1112+1920+… +98999900=______ .
12+56+1112+1920+… +98999900=（1-12）+（1-16）+（1-112）+（1-120）+… +（1-19900）=99-（12+16+112+120+130+… +19900）=99-（1-12+12-13+13-14+14-15+15-16+… +199-1100）=99-（1-1100）=99-1+1100=98+0.01=98.01...
It is proved that the function is periodic
F (x + T) = f (x), can t be negative?
Of course, and negative numbers are essentially the same as positive numbers. For example, f (x-1) = f (x), that is to say, the function values corresponding to X and X-1 are the same, so the function values corresponding to (x + 1) and (x + 1) - 1 should be the same, that is, the function values corresponding to (x + 1) and X are the same, that is, f (x + 1) = f (x)
It can be converted to a negative number
087 + 15 * 20 is equal to?
Original formula = 087 + 300 = 387
If there is no previous 0 equal to 387, do you want to write more 0
387，
Original formula = 087 + 300 = 387
Original formula = 87 + 300 = 387
Proof of periodic function
Help me prove that y = sin2x is a periodic function
Because the square can't be found, it becomes 2x, which should be the square of SiNx
According to the power reduction formula, I know. Is there any other way to find it?
Using the formula y = sin2x = (1-cos2x) / 2
Because cos2x is a periodic function and the period is π, y = (1-cos2x) / 2 is also a periodic function and the period is π
（sinx）2=（1-cos2x）/2
It's obviously a periodic function, t = Pi
Draw a picture and it will come out. The period is π. Prove it with X and (x + π). Just use the formula of trigonometric function change.
Draw image range [0, 1]
Five o'clock line drawing
714 + 15 * 62 is equal to?
714+15*62
=714+930
=1644
Hello!
714+15*62
=714+930
=1644
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Hello!
714+15*62
=714+930
=1644
If you don't understand this question, you can ask. If you are satisfied, please click "adopt as a satisfactory answer" in the lower right corner
If you have any other questions, please accept this question and click my avatar to ask for help. The answer is not easy. Please understand. Thank you.
O(∩_ Remember to adopt and help each other
I wish you progress in your study! Put it away
Multiplication and division before addition and subtraction
714+15*62
=714+930
=1644
Operations with two levels
First calculate the second level (multiplication and division), then calculate the first level addition and subtraction
714+15×62
=714+930
=1644
How to prove that a function is periodic?,
The method of proving periodic function is to define f (x) = f (x + T), that is, to use substitution to transform the complex expression in brackets into x and x plus another T, no matter how complex the expression of T is, as long as it has nothing to do with X
026 + 15 * 68 is equal to?
The answer is 1046
The answer is 1046
Multiply and divide first, then add and subtract
26+15*68
=26+1020
=1046