Angle Between 2 Vectors

The a gle betqeen 2 vectors is a way to find the distance between the 2. It is simple plug and chug into the formula. 

Put all variables into the equation and solve. 

Binomial theroem

The binomial theroem is that an equation with a power can be expanded. This would be like (x-2)^4 and you would have to expand it out into the four parts to make one whole equation. The easiest way to do this is to use pasacals triangle. 

That is all that you have to do. Start on the left with the first term to the max power. On the last equation it would be to the 4. Then decrease from left to right. Then take the right term and do the same but start on the right and go left. You decrease the power every time. That is all

Rotation of conics

4 steps

1. Plug in to cot2ø= a-c/b

A is the number infront of the x^2 term b is infornt of the xy term and c is infront of the y^2 point. 

2. Solve for x and y prime by plugin in for x=xcosø-ysinø and y=xsinø-ycosø

3. After that substitute in the original equation. 

4. Simplify and done

Determinants of Matrices

A determinant of a matrix is a constant number for a matrix. A matrix is a set of numbers in a set of brackets. 

Shortcut of 3x3 is to take the first to columns and copy them on the outside of the matrixs then take the diagonals and multiply. 

Dot product

The dot product is a constant number for any two or more vectors. A vector is a line wiht direction and magnatuide. What you do is times the x1andx2 for you first x. Then y1 and y2 for y variable. Lastly would be the z1 and z2 to get z. A dot product is the line between the two vectors. Then add all of those together

Parametric equations

A parametric equation is where the graph goes over time. The whole point is to eleminate the parametric variable t. This jusat envolves solving for x then pluging the t variable into y. 

X=t+1 y=t-1

X-1=t 

Y=x-2

Parametric graph. 

That is all

Tangnt lines

Tangent lines are a line that comes in contact with a point and has its own slope. 

Xt is slope of a graph. As explained earlier in the pictures it is just rise over run or (f(x+h)-f(x))/h. This allows one to find the tangent line. One term that someone would come across is a deritive which is really just the slope of a line or the previous equation. 

Next is the short cut to this process because it is long and lengthy. It is simple. Take the power of the variable move it down and multiply the constant by that number then decrease the power by one. Do this for each variable. On a constant without a varible will cancle out.