I can't figure out why neither of these commands (\\
or \newline
) will work to start a new line for all of my equations.
\usepackage{amsmath}
\usepackage[utf8]{inputenc}
\begin{document}
\maketitle % showing both title and author, plus and automatic date
Consider the conic section
\begin{equation}
Ax^2+Bxy+Cy^2+Dx+Ey+F=0.
\end{equation}
If $B\neq0$, then to eliminate the xy term, we rotate the axes through an acute angle $\theta$ where
\begin{equation}
\cot(2\theta)=\frac{A-C}{B}.
\end{equation}
In the equation
\begin{equation}
11x^2-24xy+4y^2+20=0,
\end{equation}
$A=11$, $B=-24$, $C=4$, $D=0$, $E=0$, and $F=20$. We will rotate the xy-axis through an angle where
\begin{equation}
\cot(2\theta)=\frac{11-4}{-24}=\frac{-7}{24}.
\end{equation}
We will replace x and y with
\begin{equation}
x=X\cos\theta-Y\sin\theta
y=X\sin\theta+Y\cos\theta.
\end{equation}
We use the multiple angle formulas for sine and cosine that come from the addition formulas for sine and cosine
\begin{equation}
\cos(2\theta)=\cos^2(\theta)-\sin^2(\theta) and
\sin(2\theta)=2\sin(\theta)\cos(\theta).
\end{equation}
equation
is for one line equation. For multi line equations you need to use amsath environments likegather
,align
,multline
,split
etc. Welcome to TeX.SE!equation
environments. This will always fail as blank lines cannot appear inequation
environments