Function en, minimum positive period What is the minimum positive period of y = 2Sin μ x

Function en, minimum positive period What is the minimum positive period of y = 2Sin μ x

T=2π/w=2π/π=2；

It is urgent to find the minimum positive period and the maximum value of the sum square of the plus cosine of a given function

（sinx+cosx）²=sin²x+2sinxcosx+cos²x=1+2sinxcosx=1+sin2x
So the minimum positive period is π and the maximum is 1 + 1 = 2
I wish: progress in learning!

How to calculate the minimum positive period of a function

As long as it is proved that f (x + T) = f (x) is constant in the domain of function definition, and t is the minimum energy
If f (x + T) = f (x) holds, the minimum positive period of the function is t

How to calculate the minimum positive period of a function
How to calculate the minimum positive period of y = 2cos ^ 2 (2x-1)?

Because the minimum positive period of 2cos ^ 2 (α) = 1 + Cos2 α y = 1 + cos (4x-2) function is 2 π / w = 2 π / 4 = π / 2

Find the minimum positive period and maximum minimum value of function f (x)
Find the function f (x) = (sin ^ 4x + cos ^ 4x + sin ^ 2xcos ^ 2x) / (2-sin2x)
The minimum positive period and the maximum minimum of

Analysis: F (x) = {[(SiNx) ^ 2 + (cosx) ^ 2] ^ 2-2 (sinxcosx) ^ 2 + (sinxcosx) ^ 2} / (2-sin2x)
=[1-(sinxcosx)^2]/(2-2sinxcosx)
=(1+sinxcosx)(1-sinxcosx)/2(1-sinxcosx)
=1/2+sinxcosx/2
=sin2x/4+1/2
The minimum positive period T = 2 π / 2 = π
ymax=3/4,ymin=1/4

If the minimum positive period of the function y = acosax-1 is π, then the minimum value of the function?

A is equal to 2, so the minimum value of Y is - 3

The minimum positive period of function tan2x

Let me tell you a formula
The minimum positive period of tangent function is t = π / W. in tan2x function, w = 2 (W is the coefficient before x), t = π / 2
If you don't understand, ask again

The basic characteristics of periodic function

① Periodic function: for the function f (x), if there is a non-zero constant t such that when x takes every value in the domain, f (x + T) = f (x), then the function f (x) is called a periodic function. The non-zero constant T is called the period of the function. If there is not enough space, see resources

Periodic function problem
The odd function f (x-1.5) = f (x + 1.5), f (2) = 0 on R to find the zero point of F (x) in the interval (0,6)

The period is 3 F (2) = f (5) = f (1) = f (4) = 0
So there are four

Transformation methods of several common expressions of logic function

Transformation of logical function expression
There are two common methods to convert an arbitrary logic function expression into a standard expression, one is algebraic conversion, the other is truth table conversion;
1、 Algebraic transformation method
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The so-called algebraic transformation method is to use axioms, theorems and rules of logical algebra to transform function expression from one form to another
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1. Find the standard and - or expression of a function

Step 1: transform the function expression into a general and - or expression

Step 2: repeatedly use x = x (y + y) to expand the "and" of all non minimum terms in the expression to the minimum term;
For example, convert the following logical function expression to a standard and - or expression
Step 1: transform the function expression into an and - or expression

=(A+B)(B+C)+AB
=A·B+A·C+B·C+A·B
Step 2: expand the "and term" in the "and - or" formula to the minimum term. Specifically, if a "and term" is missing function variable y, then (y + y) is used to associate with this term and split it into two terms
F(A,B,C)
=A·B(C+C)+AC(B+B)+(A+A)BC+AB(C+C)
=A·B·C+A·B·C+A·B·C+A·B·C+A·B·C+A·B·C+A·B·C+A·B·C
=A·B·C+A·B·C+A·B·C+A·B·C+A·B·C
The abbreviation of "and - or" is
F(A,B,C)
=m0+m1+m3+m6+m7
=∑m(0,1,3,6,7)
When the function expression is already an and - or expression, the second step can be carried out directly
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2. Find a function standard or and expression
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Step 1: convert the function expression into a general or and expression
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The second step: using the theorem a = (a + b) (a + b) repeatedly to expand the or term of all non maximum terms in the expression to the maximum term
For example, transform the following logical function expression into a standard or and expression
&#The first step is to transform the function expression into an or and expression;
=(A+B)(A+C)+BC
=[(A+B)(A+C)+B]·[(A+B)(A+C)+C]
=(A+B+B)(A+C+B)(A+B+C)(A+C+C)
=(A+B)(A+B+C)(A+B+C)
The second step is to extend the non maximum term in the expression to the maximum term
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F(A,B,C)
=(A+B)(A+B+C)(A+B+C)
=(A+B+C)(A+B+C)(A+B+C)(A+B+C)
=(A+B+C)(A+B+C)(A+B+C)
The short form of the standard or and expression is
F(A,B,C)=M3M6M7=∏M(3,6,7)
When the given function is already an "or - and" expression, the second step can be carried out directly;
2、 Transformation method of truth table;
The truth table of a logic function has a one-to-one correspondence with its minimum term expression. Suppose that there are k groups of variables in the truth table of function f such that the value of F is 1, and the value of F is 0 under other variables, then the minimum term expression of function f consists of K minimum terms corresponding to the values of these K groups of variables. Therefore, the minimum term expression can be written out through the truth table of function
1. Find the standard "and - or" formula of function
Specifically: in the truth table, the minimum term corresponding to the value combination of variables whose function value is 1 can form the standard "and - or" formula of a function;
For example, the function expression f (a, B, c) = AB + BC is transformed into the minimum term expression
&#Solution: first, list the truth table of F, as shown in table 2.6, and then directly write the expression of the minimum term of F according to the truth table;
F(A,B,C)=∑m(2,4,5,6)
2. Find the standard "or - and" formula of function
There is also a one-to-one correspondence between the truth table of a logic function and its maximum term expression. Suppose that in the truth table of function f, there are k groups of variables with values such that the value of F is 0, and the value of F under other variables is 1, then the maximum term expression of function f is composed of K maximum term "phase and" corresponding to the values of these K groups of variables, The expression of the maximum term of the function can be written directly according to the truth table;
Specific: in the truth table, if the maximum term corresponding to the value combination of variables whose function value is 0 is "and", the standard "or - and" formula of a function can be formed;
For example, the function expression f (a, B, c) = a · C + a · B · C is expressed in the form of maximum term expression
First, the truth table of F is listed, as shown in table 2.7. Then, the maximum term expression of F is written directly according to the truth table;
F(A,B,C)=∏M(0,2,5,6,7)
Because there is a one-to-one correspondence between the truth table of a function and the two standard expressions of a function, and the truth table of any logic function is unique, so the two standard forms of any logic function are unique. This brings us great convenience to analyze and study logic functions
I hope I can help you,