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In 2022, high school must recite 88 mathematical formulas, and all the mathematical formulas in high school will be sorted out.
What are the 88 mathematical formulas that senior high school must recite in 2022? I sorted out the relevant information, hoping to help everyone! ?

In 2022, what are the round formulas of mathematical formulas that high school must recite?

1, circle volume = 4/3(π)(R3)

2. Area =(π)(R2)

3. Perimeter = 2(π)r

4. The standard equation of a circle (x-a)2+(y-b)2=r2(a, B) is the center coordinate.

5. Circle X2+Y2+DX+EY+F = 0d2+E2-4f > 0

Elliptic formula

1, ellipse circumference formula: l=2πb+4(a-b).

2. ellipse circumference's Theorem: The circumference of an ellipse is equal to the short axis of an ellipse, and the circumference of a circle with a radius of (2πb) plus four times the difference between the long axis (a) and the short axis (b) of an ellipse.

3. Elliptic area formula: s=πab

4. Ellipse area theorem: the area of an ellipse is equal to π times the product of the major semi-axis length (a) and the minor semi-axis length (b) of the ellipse.

Although there is no ellipse πT in the above ellipse circumference sum area formula, both formulas are derived from ellipse π t. ..

Two-angle sum formula

1、sin(a+b)= Sina cosb+cosasinbsin(a-b)= Sina cosb-sinbcosa

2、cos(a+b)= cosa cosb-Sina sinb cos(a-b)= cosa cosb+Sina sinb

3、tan(a+b)=(tana+tanb)/( 1-tana tanb)tan(a-b)=(tana-tanb)/( 1+tana tanb)

4、ctg(a+b)=(ctgactgb- 1)/(ctg b+ctga)ctg(a-b)=(ctgactgb+ 1)/(ctg b-ctga)

Double angle formula

1、tan2a = 2 tana/( 1-tan2a)ctg2a =(ctg2a- 1)/2c TGA

2、cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a

half-angle formula

1、sin(a/2)=√(( 1-cosa)/2)sin(a/2)=-√(( 1-cosa)/2)

2、cos(a/2)=√(( 1+cosa)/2)cos(a/2)=-√(( 1+cosa)/2)

3、tan(a/2)=√(( 1-cosa)/(( 1+cosa))tan(a/2)=-√(( 1-cosa)/(( 1+cosa))

4、ctg(a/2)=√(( 1+cosa)/(( 1-cosa))ctg(a/2)=-√(( 1+cosa)/(( 1-cosa))

Sum difference product

1、2 Sina cosb = sin(a+b)+sin(a-b)2 cosa sinb = sin(a+b)-sin(a-b)

2、2 cos ASB = cos(a+b)-sin(a-b)-2 sinasinb = cos(a+b)-cos(a-b)

3、Sina+sinb = 2 sin((a+b)/2)cos((a-b)/2 cosa+cosb = 2 cos((a+b)/2)sin((a-b)/2)

4、tana+tanb = sin(a+b)/cosacosbtana-tanb = sin(a-b)/cosacosb

5、ctga+ctgbsin(a+b)/Sina sin b-ctga+ctgbsin(a+b)/Sina sinb

arithmetic series

1, arithmetic progression's general formula is:

an = a 1+(n- 1)d( 1)

2. 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, and 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.

3. From the definition and general formula of arithmetic progression, the first n terms and formulas can also be deduced:

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

geometric series

The general formula of 1 and geometric series is: an = a 1 * q (n- 1).

2. the sum formula of the first n items is: sn = [a1(1-q n)]/(1-q)

And the relationship between any two terms am and an an = am q (n-m).

3. A1an = a2an-1= a3an-2 = … = akan-k+1,k ∈ {1 can be deduced from the definition of geometric series, the general term formula and the first n terms.

4. If m, n, p, q∈N*, there is: AP AQ = am an.

Equal ratio mean: AQ AP = 2 ARAR is the equal ratio mean of AP and AQ.

If π n = A 1 A2 … an, then π 2n- 1 = (an) 2n- 1, π 2n+1= (an+1) 2n+1.

In addition, each term is a geometric series with positive numbers, and the same base number is taken to form a arithmetic progression; On the other hand, taking any positive number c as the cardinal number and a arithmetic progression term as the exponent, a power energy is constructed, which is a geometric series. In this sense, we say that a positive geometric series and an arithmetic series are isomorphic.

Properties: ① if m, n, p, q∈N, m+n = p+q, then am an = AP * AQ;;

(2) In geometric series, every k term is added in turn and still becomes a geometric series.

G is the median term in the equal proportion of A and B, and G 2 = AB (G ≠ 0).

In geometric series, the first term A 1 and the common ratio q are not zero.

parabola

1, parabola: y=ax*+bx+c is the square of y = ax plus bx plus c.

A>0, parabolic opening upward; At a & lt0°, the parabolic opening is downward; When c=0, the parabola passes through the origin; When b=0, the axis of symmetry of parabola is the Y axis.

2. Vertex y=a(x+h)*+k means that Y is equal to A times the square of (x+h) +k, -h is X of vertex coordinates, and K is Y of vertex coordinates, which is generally used to find the maximum and minimum values.

3. Parabolic standard equation: y 2 = 2px, which means that the focus of parabola is on the positive semi-axis of X, and the focal coordinate is (p/2,0).

4. The directrix equation is x=-p/2. Because the focus of parabola can be on any half axis, there is a standard equation for * * *: y 2 = 2pxy 2 =-2pxy 2 =-2pxy.

What are the necessary mathematical formulas in senior high school? 1. sine and cosine theorems.

Sine theorem: a/sinA=b/sinB=c/sinC=2R R is the radius of the circumscribed circle of a triangle.

Cosine theorem: a2=b2+c2-2bc*cosA

Second, the inductive formula

One: Let α be an arbitrary angle, and the values of the same trigonometric function with the same angle of the terminal edge are equal;

sin(2kπ+α)= sinα(k∈Z)cos(2kπ+α)= cosα(k∈Z)tan(2kπ+α)= tanα(k∈Z)cot(2kπ+α)= cotα(k∈Z)

2. Let α be any angle, and the relationship between the trigonometric function value of π+α and the trigonometric function value of α;

sin(π+α)=-sinαcos(π+α)=-cosαtan(π+α)= tanαcot(π+α)= cotα

Third, the relationship between arbitrary angle α and trigonometric function value of-α;

sin(-α)=-sinαcos(-α)= cosαtan(-α)=-tanαcot(-α)=-cotα

4. The relationship between π-α and the trigonometric function value of α can be obtained by Formula 2 and Formula 3:

sin(π-α)= sinαcos(π-α)=-cosαtan(π-α)=-tanαcot(π-α)=-cotα

5.2 The relationship between π-α and the trigonometric function value of α can be obtained by formula 1 and formula 3:

sin(2π-α)=-sinαcos(2π-α)= cosαtan(2π-α)=-tanαcot(2π-α)=-cotα

6. The relationship between π/2α and 3 π/2 α and the value of α trigonometric function;

Third, the summation formula of two angles

sin(A+B)= Sina cosb+cosa sinb sin(A-B)= Sina cosb-sinb cosa

cos(A+B)= cosa cosb-Sina sinb cos(A-B)= cosa cosb+Sina sinb

tan(A+B)=(tanA+tanB)/( 1-tanA tanB)tan(A-B)=(tanA-tanB)/( 1+tanA tanB)

ctg(A+B)=(ctgActgB- 1)/(ctg B+ctgA)ctg(A-B)=(ctgActgB+ 1)/(ctg B-ctgA)

Four, the double angle formula

tan2A = 2 tana/( 1-tan2A)ctg2A =(ctg2A- 1)/2c TGA

cos2a = cos2a-sin2a = 2 cos2a- 1 = 1-2 sin2a

Verb (abbreviation of verb) half-angle formula

sin(A/2)=√(( 1-cosA)/2)sin(A/2)=-√(( 1-cosA)/2)

cos(A/2)=√(( 1+cosA)/2)cos(A/2)=-√(( 1+cosA)/2)

tan(A/2)=√(( 1-cosA)/(( 1+cosA))tan(A/2)=-√(( 1-cosA)/(( 1+cosA))

ctg(A/2)=√(( 1+cosA)/(( 1-cosA))ctg(A/2)=-√(( 1+cosA)/(( 1-cosA))

Six, sum and difference product

2 Sina cosb = sin(A+B)+sin(A-B)2 cosa sinb = sin(A+B)-sin(A-B)

2 cosa cosb = cos(A+B)-sin(A-B)-2 sinasinb = cos(A+B)-cos(A-B)

sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2 cosA+cosB = 2 cos((A+B)/2)sin((A-B)/2)

tanA+tanB = sin(A+B)/cosa cosb tanA-tanB = sin(A-B)/cosa cosb

ctgA+ctgBsin(A+B)/Sina sinb-ctgA+ctgBsin(A+B)/Sina sinb

Seven, the sum of the first n terms of some series.

1+2+3+4+5+6+7+8+9+…+n = n(n+ 1)/2 1+3+5+7+9+ 1 1+ 13+ 15+…+(2n- 1)= N2

2+4+6+8+ 10+ 12+ 14+…+(2n)= n(n+ 1) 12+22+32+42+52+62+72+82+…+N2 = n(n+ 1)(2n+ 1)/6

13+23+33+43+53+63+…n3 = N2(n+ 1)2/4 1 * 2+2 * 3+3 * 4+4 * 5+5 * 6+6 * 7+…+n(n+ 1)= n(n+ 1)(n+2)/3