Two-angle sum formula

sin(A+B) = sinAcosB+cosAsinB

sin(A-B) = sinAcosB-cosAsinB？

cos(A+B) = cosAcosB-sinAsinB

cos(A-B) = cosAcosB+sinAsinB

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

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

cot(A+B)=(cotA cotB- 1)/(cot B+cotA)？

cot(A-B)=(cotA cotB+ 1)/(cot b-cotA)

Double angle formula

Sin2A=2SinA？ Kosa

cos2a=cosa^2-sina^2= 1-2sina^2=2cosa^2- 1

tan2A=2tanA/( 1-tanA^2)

(Note: SinA^2 is the square of Sina sin2(A).

Inductive formula: sin(-α) = -sinα.

cos(-α) = cosα

sin(π/2-α) = cosα

cos(π/2-α) = sinα

sin(π/2+α) = cosα

cos(π/2+α) = -sinα

Sine (π-α) = Sine α

cos(π-α) = -cosα

Sine (π+α) =-Sine α

cos(π+α) = -cosα

tanA= sinA/cosA

tan(π/2+α)=-cotα

tan(π/2-α)=cotα

tan(π-α)=-tanα

tan(π+α)=tanα

2. Multiplication principle: n = n 1 N2 NN

3. addition principle: m = m1+m2+...+mm.

4. permutation and combination formula (you can check it) note: full permutation formula: when m = n, it is full permutation PNN = n (n-1) (n-2) … 3.2.1= n!

Report Supplementary Respondents 2009-07-1618:10. According to the coordinate axis where the focus is located, the ellipse has two standard equations:

1) when the focus is on the x axis, the standard equation is: x2/a2+y2/B2 =1(a >; b & gt0)

2) When the focus is on the Y axis, the standard equation is: x2/b2+y2/a2 =1(a > b >; 0)

2. Sequence restriction:

Let it be a series. If there is a constant a, when n increases infinitely, an approaches (approaches) to A infinitely, which means that the series converges, and A is called the limit of the series, or it means that the series converges to A, which is recorded as Li Man = A. Or: an→a, when n→∞.

3. Limit algorithm (or related formula):

lim(f(x)+g(x))=limf(x)+limg(x)

lim(f(x)-g(x))=limf(x)-limg(x)

lim(f(x)*g(x))=limf(x)*limg(x)

Lim (f (x)/g (x)) = LIMF (x)/LIMG (x) (LIMG (x) is not equal to 0).

lim(f(x))^n=(limf(x))^n

Only when the above limf(x) limg(x) exists can it be established.

lim( 1+ 1/x)^x =e

x→∞

Infinity and infinitesimal:

A series (limit) is infinitely close to 0, which is an infinitesimal series (limit).

Infinite sequence and infinitesimal sequence are reciprocal.

Two important limitations:

1、lim sin(x)/x = 1，x→0

2.lim (1+ 1/x) x = e, x→∞ (e≈2.7 1828 18 ..., irrational number).

4. Want to study mathematics in university and master calculus formula:

① C'=0(C is a constant function);

②(x^n)'= nx^(n- 1)(n∈q)；

③(sinx)' = cosx；

④(cosx)' =-sinx；

⑤(e^x)' = e^x；

⑥ (a x)' = (a x) * ina (ln is natural logarithm)

⑦ (Inx)' = 1/x(ln is natural logarithm)

⑧ (logax)' =( 1/x)*logae, (a>0 and a is not equal to 1)

Add something. The above formula can not replace constants, but only functions. People who are new to derivatives often ignore this point, which leads to ambiguity. We should pay more attention to it.

(3) Four algorithms of derivative:

①(u v)'=u' v '

②(uv)'=u'v+uv '

③(u/v)'=(u'v-uv')/ v^2

Logarithmic properties and arithmetic loga (Mn) = logam+loganglogamn = nlogam (n ∈ r) exponential function logarithmic function

(1) y = ax (a > 0, a≠ 1) is called exponential function.

(2)x∈R，y>0

Image transfer (0, 1)

When a > 1, x > 0, y > 1; When x 1, y = ax is an increasing function.

0 < a < 1, y = ax is a decreasing function (1), and y = logax (a > 0, a≠ 1) is a logarithmic function.

(2)x>0，y∈R

Image transfer (1, 0)

When a > 1, x > 1, y > 0; 0 1, y = logax is increasing function.

0 < a < 1, y = logax is a decreasing function.

Exponential equation and logarithmic equation

fundamental form

logaf(x)=b f(x)=ab(a>0，a≠ 1)

Same bottom type

logaf(x)= logag(x)f(x)= g(x)> 0(a > 0，a≠ 1)

Substitution type f (ax) = 0 or f (logax) = 0.

Step 2: Order

Basic concept of arithmetic progression of sequence.

The general formula of (1) series an = f (n)

(2) Recursive formula of sequence

(3) The relationship between the general term formula of the sequence and the sum of the first n terms an+1-an = d.

an=a 1+(n- 1)d

A, a and b are equal. 2A = A+B

m+n=k+l am+an=ak+al

Common summation formulas of geometric series

an=a 1qn_ 1

The proportion of A, G and B is equal G2 = AB.

M+n = k+ Raman = akal3, inequality

Basic properties of inequalities Important inequalities

a>b bb，b>c

a>b a+c>b+c

a+b>c a>c-b

a>b，c>d

a>b，c>0 ac>bc

a>b，c0，c>d>0 acb>0 dn>bn(n∈Z，n> 1)

a>b>0 > (n∈Z，n> 1)

(a-b)2≥0

a，b∈R a2+B2≥2ab | a |-| b |≤| a b |≤| a |+| b |

Basic methods of proving inequality

comparative law

(1) To prove the inequality A > B (or A < B), just prove it.

A-b > 0 (or a-b < 0 =)

(2) if B > 0, to prove that A > B, just prove that,

To prove a < b, prove it.

Synthesis method is a method to deduce the inequality to be proved (from cause to effect) from the known or proved inequality according to the nature of inequality.

Analytical method is to seek the sufficient conditions for the conclusion to be established, and gradually seek the sufficient conditions for the required conditions to be established until the required conditions are known to be correct, which is obviously manifested as "holding the fruit"

4. Complex number

Algebraic form triangular form

A+bi =c+ Adi = c, B = D (A+Bi)+(C+Di) = (A+C)+(B+D) I.

(a+bi)-(c+di)=(a-c)+(b-d)i

(a+bi)(c+di )=(ac-bd)+(bc+ad)i

a+bi = r(cosθ+isθ)

r 1 =(cosθ 1+isθ 1)？ R2(cosθ2+isθ2)

=r 1？ R2[cos(θ 1+θ2)+isin(θ 1+θ2)]

[r(cosθ+sinθ)]n = rn(cosnθ+isinnθ)k = 0， 1，…，n- 1

5. permutation, combination and binomial theorem

The binomial theorem of permutation and combination in binomial expansion (1) is equal to the binomial coefficient of "equidistant" at both ends.

(2) If the power exponent of the binomial is even, the binomial coefficient of the middle term is the largest; If the power exponent of binomial is odd, the binomial coefficients of the middle two terms are equal and the largest.

6. Complex number

Geometric Significance of Modulus, Radial Angle and * * * Yoke Complex Number

|z 1z2|=|z 1|？ The geometric meaning of |z2|( 1) complex addition and subtraction is the synthesis and decomposition of vectors (parallelogram rule or triangle rule).

(2) The geometric meaning of multiplication, division and power of complex numbers can be obtained through its trigonometric operation.

(3) The geometric meaning of the n-th square root of a complex number is that the points corresponding to the n-th square root are evenly distributed on the circumference with the origin as the center and the radius as the radius.

trigonometric function

Angle relation of arc system

1 = 1 rad

Arc length formula l = | α| rsin2α+cos2α = 1.

1+tan2α=sec2α

1+COT2α = COS2α I hope you are satisfied.