TODO: Note the equations. Parabola A parabola is the set of all points that are equidistant from a point (the focus) and a fixed line...
If two lines are perpendicular, then \(m_{1}m_{2}=-1\) where \(m_{i}\) is the slope of the line. Proof Without Trigonometry Here’s the...
Here is an example of proving something using induction in Sage. Suppose we want to prove that: \begin{equation*}...
Formula for \(\cos(\alpha-\beta)\) Consider the unit circle below: Here, we make \(\overline{AB}=\overline{CD}\), so they have the...
We know that: \begin{equation*} \sum_{k=1}^{n} k=\frac{n(n+1)}{2} \end{equation*} We want to find the expression for \begin{equation*}...
Say we want the roots of \(z^{n}=1\). Let \(z=re^{i\theta}\). Then \(z^{n}=r^{n}e^{in\theta}=1\). We immediately see that \(r=1\). Thus...