How to left align equation?

Question

I'm trying to left align the following equation so that it's on the same line as 3 (a).

\begin{enumerate}
\item 
\begin{align*}

|\gamma(t)| &= [\gamma(t) \cdot \gamma(t)]^{\frac{1}{2}}\\
&=[(cos(t)p + sin(t)v) \cdot (cos(t)p + sin(t)v)]^{\frac{1}{2}}\\
&=[cos^2(t)(p \cdot p) + sin^2(t)(v \cdot v) + 2cos(t)sin(t)(p \cdot v) ]^{\frac{1}{2}}

\end{align*}
\end{enumerate}

Edit: After the fix, this is the result I get:

    \item
    \begin{enumerate}
        \item 
        $\begin{aligned}[t]
        |\gamma(t)| &= [\gamma(t) \cdot \gamma(t)]^{\frac{1}{2}}, \forall t \in \mathbb{R}\\
        &=[(\cos(t)p + \sin(t)v) \cdot (\cos(t)p + \sin(t)v)]^{\frac{1}{2}}\\
        &=[\cos^2(t)(p \cdot p) + \sin^2(t)(v \cdot v) + 2\cos(t)\sin(t)(p \cdot v) ]^{\frac{1}{2}}\\
        &=[\cos^2(t)(1) + \sin^2(t)(1) + 2\cos(t)\sin(t)(0) ]^{\frac{1}{2}}\\
        &=[\cos^2(t) + \sin^2(t)]^{\frac{1}{2}}\\
        &=1
        \end{aligned}$

        \item
        $\begin{aligned}
        |\gamma'(t)| &= [\gamma'(t) \cdot \gamma'(t)]^{\frac{1}{2}}, \forall t \in \mathbb{R}\\
        &=[(\cos(t)p + \sin(t)v)' \cdot (\cos(t)p + \sin(t)v)']^{\frac{1}{2}}\\
        &=[(-\sin(t)p + \cos(t)v) \cdot (-\sin(t)p + \cos(t)v)]^{\frac{1}{2}}\\
        &=[\sin^2(t)(p \cdot p) + \cos^2(t)(v \cdot v) - 2\cos(t)\sin(t)(p \cdot v) ]^{\frac{1}{2}}\\
        &=[\sin^2(t)(1) + \cos^2(t)(1) - 2\cos(t)\sin(t)(0) ]^{\frac{1}{2}}\\
        &=[\sin^2(t) + \cos^2(t)]^{\frac{1}{2}}\\
        &=1
        \end{aligned}$

Answer 1

your question was asked so many times that it is for sure duplicate ... anyway, try the following:

\documentclass{article}
\usepackage{amsmath}
\usepackage{enumitem}

\begin{document}
\begin{enumerate}[label=(\alph*)]
\item   $\begin{aligned}[t] % "[t]" align the first line of `aligned` with
                            % item label text line
|\gamma(t)| & = [\gamma(t) \cdot \gamma(t)]^{\frac{1}{2}}\\
            & = [(\cos(t)p + \sin(t)v) \cdot (\cos(t)p + \sin(t)v)]^{\frac{1}{2}}\\
            & = [\cos^2(t)(p \cdot p) + \sin^2(t)(v \cdot v) 
                    + 2\cos(t)\sin(t)(p \cdot v) ]^{\frac{1}{2}}
        \end{aligned}$
\item   $\begin{aligned}[t] % <--- observe "[t]" 
|\gamma(t)| & = [\gamma(t) \cdot \gamma(t)]^{\frac{1}{2}}       \\
            & = [(\cos(t)p + \sin(t)v) \cdot (cos(t)p + \sin(t)v)]^{\frac{1}{2}}\\
            & = [\cos^2(t)(p \cdot p) + \sin^2(t)(v \cdot v)
                    + 2cos(t)\sin(t)(p \cdot v) ]^{\frac{1}{2}} \\
            & = [p^2\cos^2(t) + v^2\sin^2(t) 
                    + 2pv\cos(t)\sin(t)]^{\frac{1}{2}} 
        \end{aligned}$
\end{enumerate}
\end{document}

edit (i): now i notice that you use sin and cos as variables and not as math operators. now i correct this too.

edit (ii): to show the importance of option [t] (top align) i add another item to the list. in the comments in the program I also added a brief explanation.

Answer 2

\documentclass[preview,border=12pt,varwidth]{standalone}
\usepackage{mathtools}
\begin{document}
\begin{enumerate}
\item This is the setting you are interested in?\\
$\!
\begin{aligned}[t]
|\gamma(t)| &= [\gamma(t) \cdot \gamma(t)]^{\frac{1}{2}}\\
&=[(cos(t)p + sin(t)v) \cdot (cos(t)p + sin(t)v)]^{\frac{1}{2}}\\
&=[cos^2(t)(p \cdot p) + sin^2(t)(v \cdot v) + 2cos(t)sin(t)(p \cdot v) ]^{\frac{1}{2}}
\end{aligned}
$
\end{enumerate}
\end{document}

Edit:

Due to my laziness, I leave the code above as the current condition. As a result, I have to assume that sin used above is the product of s, i, and n. This assumption is also applied to the cos.

Answer 3

If you want to both center and number a mathematical expression, you have to insert a displayed equation, not an in-line one. A solution was proposed by Philippe Goutet in his answer to the question Vertical alignment of align* in enumerate.