🗺️

公式大全

熟習公式不是一切，卻是基本

‣

Algebra

‣

Laws of Indices

\forall a,b,m,n\in\R\\ a^m\cdot a^n=a^{m+n}\\(a\cdot b)^n=a^nb^n\\(a^m)^n=a^{mn}\\a^{-n}=\frac{1}{a^n}\\a^\frac{m}{n}=\sqrt[n]{a^m}

‣

Quadratics

\forall a,b,c\in\R\\ax^2+bx+c=0\\ x=\frac{-b±\sqrt{\Delta}}{2a}\ ,\ \Delta=b^2-4ac

\forall \alpha,\beta,\in C \\a\alpha^2+b\alpha+c=0=a\beta^2+b\beta+c=0\\\alpha+\beta=\frac{-b}{a}\\\alpha\times\beta=\frac{c}{a}\\|\alpha-\beta|=\frac{\sqrt\Delta}{a}

y=ax^2+bx+c\\y=a(x-h)^2+k\\ h=\frac{-b}{2a}\ ,\ k=c-ah^2

‣

Polynomials

‣

Logarithms

‣

Sequences

‣

Geometry

‣

Right Triangles

a^2+b^2=c^2\\\sin\theta=\frac{b}{c}\ ,\ \cos\theta=\frac{a}{c}\\\tan\theta=\frac{b}{a}\ \ \,\ \ \forall\ a,b,c\ \in\R^+\ ,\ \ c≤a+b

‣

General Triangles

S_{\Delta ABC}=\frac{1}{2}ab\sin\angle C=\sqrt{s(s-a)(s-b)(s-c)}\ ,\ s=\frac{a+b+c}{2}\\\frac{a}{\sin\angle A}=\frac{b}{\sin\angle B}=\frac{c}{\sin\angle c}=2R\\a^2+b^2-2ab\cos\angle C=c^2

‣

Circles

‣

Area

‣

Volume

‣

Co-Geo

‣

Data

← back to Home