Summary of key knowledge of senior two mathematics in single education edition
Formula 1: Let α be an arbitrary angle, and the values of the same trigonometric functions with the same terminal angles are equal:
sin(2kπ+α)=sinα
cos(2kπ+α)=cosα
tan(2kπ+α)=tanα
cot(2kπ+α)=cotα
Equation 2:
Let α be an arbitrary angle, and the relationship between the trigonometric function value of π+α and the trigonometric function value of α;
Sine (π+α) =-Sine α
cos(π+α)=-cosα
tan(π+α)=tanα
cot(π+α)=cotα
Formula 3:
The relationship between arbitrary angle α and the value of-α trigonometric function;
Sine (-α) =-Sine α
cos(-α)=cosα
tan(-α)=-tanα
Kurt (-α) =-Kurt α
Equation 4:
The relationship between π-α and the trigonometric function value of α can be obtained by Formula 2 and Formula 3:
Sine (π-α) = Sine α
cos(π-α)=-cosα
tan(π-α)=-tanα
Kurt (π-α) =-Kurt α
Formula 5:
The relationship between 2π-α and the trigonometric function value of α can be obtained by formula 1 and formula 3:
Sine (2π-α)=- Sine α
cos(2π-α)=cosα
tan(2π-α)=-tanα
Kurt (2π-α)=- Kurt α
Equation 6:
The relationship between π/2 α and 3 π/2 α and the trigonometric function value of α;
sin(π/2+α)=cosα
cos(π/2+α)=-sinα
tan(π/2+α)=-cotα
cot(π/2+α)=-tanα
sin(π/2-α)=cosα
cos(π/2-α)=sinα
tan(π/2-α)=cotα
cot(π/2-α)=tanα
sin(3π/2+α)=-cosα
cos(3π/2+α)=sinα
tan(3π/2+α)=-cotα
cot(3π/2+α)=-tanα
sin(3π/2-α)=-cosα
cos(3π/2-α)=-sinα
tan(3π/2-α)=cotα
cot(3π/2-α)=tanα
(higher than k∈Z)
Overview of Key Knowledge of Senior Two Mathematics in People's Education Press
an = a 1+(n- 1)d( 1)
The first n terms and formulas are:
Sn=na 1+n(n- 1)d/2 or Sn=n(a 1+an)/2(2).
It can be seen from the formula (1) that an is a linear function (d≠0) or a constant function (d = 0) of n, and (n, an) is arranged in a straight line. According to formula (2), Sn is a quadratic function (d≠0) or a linear function (d =
Arithmetic average in arithmetic progression: generally set as Ar, Am+an=2Ar, so Ar is the arithmetic average of Am and An.
The relationship between any two am and an is:
an=am+(n-m)d
It can be regarded as arithmetic progression's generalized general term formula.
From arithmetic progression's definition, general term formula and the first n terms formula, we can also deduce that:
a 1+an = a2+an- 1 = a3+an-2 =…= AK+an-k+ 1，k∈{ 1，2，…，n}
If m, n, p, q∈N*, m+n=p+q, then there is.
am+an=ap+aq
Sm- 1=(2n- 1)an，S2n+ 1 =(2n+ 1)an+ 1
Sk, s2k-sk, s3k-s2k, …, snk-s (n- 1) k … or arithmetic progression, and so on.
Sum = (first item+last item) * number of items ÷2
Number of items = (last item-first item) ÷ tolerance+1
First Item =2, Number of Items-Last Item
Last item =2, number of items-first item
Number of items = (last item-first item)/tolerance+1
If the ratio of each term in a series from the second term to the previous term is equal to the same non-zero constant, the series is called geometric series. This constant is called the common ratio of geometric series, which is usually expressed by the letter q (q≠0). Note: When q= 1, an is a constant series.
A summary of the key knowledge of senior two mathematics in three-person education edition
Classification of solving inequality problems
Solve a linear inequality of one variable.
Solve a quadratic inequality in one variable.
Inequalities that can be reduced to one-dimensional linear or one-dimensional quadratic inequalities.
(1) to solve the unary higher inequality;
② Solving fractional inequality;
③ Solving irrational inequalities;
④ Solving exponential inequality;
⑤ Solving logarithmic inequality;
6. Solve inequalities with absolute values;
⑦ Solve inequality.
Pay special attention to the following points when solving inequalities:
Correctly apply the basic properties of inequality.
Correctly apply the increase and decrease of power function, exponential function and logarithmic function.
Pay attention to the range of unknown quantities in algebraic expressions.
Homotopy solution of inequality
|f(x)|0)
|f(x)| >g(x)
① and f(x)>G(x) or f(x)ag(x) and f(x) > when 0aG(x) and f(x), g(x) is the same solution.