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