concepts

Trig

sin, cos, tan, cot

domain and range

their graph and transformation

Vector

intersection of one line and plane: 1. since we have the line \(r=a+\lambda b\) and the plane \(r \cdot n = A\) 2. we use \((a+\lambda b) \cdot n = A\), solve for \(\lambda\)

find intersection line of two planes: - with hand: 1. direction vector is the cross product of the two planes’ normal 2. find one exact point of intersection by assuming a point at \(z=0\), and solve the system equations of two planes 3. use that point to find the position vector of the intersection line - with GDC: 1. get two points, \(z=0\) and \(z=1\) 2. use two points to find the line

System of Equation

system of linear equation: 1. has one solution (consistent and no redundancy) 2. no solution (contradiction) 3. infinite solution (consistent but redundancy)

常见敌人/应对方式

奇怪的等式证明？两边凑，二倍角公式正反用（二分之一倍角公式）

radian的弧长和扇形面积公式要小心

\(\cos \theta = \sin (\frac{\pi}{2} - \theta)\)