Problem with aligning text but not equations

Question

\begin{align*}
\\ \text{Let } arcsin(x) & = \theta
\\\text{But } \theta \text{ is a function of x so we can write }
\\ arcsin(x) & = \theta(x)
\\ x & = sin(\theta(x))
\\ \frac{d}{dx}x & = \frac{d}{dx}sin(\theta(x))

\\ \text{Imagine f(x) = sin(x) and g(x) = } \theta(x).
\\ \text{Thus, f'(g(x))g'(x) = cos(} \theta(x))\theta'(x).
\\\text{So overall, you differentiated sin(} \theta) \text{ with respect to } \theta.
\end{align*} 

I wrote the above in Notion. I managed to align all my equations however, my text is not aligned. I am struggling to fix this.

I am new to LaTeX and to this community so I apologise if my question is in the wrong format.

Answer 1

I suggest you take the first two lines and the last line out of the align* environment entirely and place one of the intermediate lines in an \intertext wrapper. (BTW, I'm addressing only the typesetting issues, not the mathematics involved. Hence, I'm not going to comment on \frac{d}{dx}x.)

Oh, by all means please write \sin, \cos, and \arcsin rather than just sin, cos, and arcsin.

\documentclass{article}
\usepackage{amsmath} % for 'align*' env. and '\intertext' macro
\begin{document}
\noindent
Let $\arcsin(x) = \theta$. Because $\theta$ is a function of $x$, we can write
\begin{align}
\arcsin(x) &= \theta(x) \ 
x &= \sin(\theta(x)) \ 
\frac{d}{dx}x &= \frac{d}{dx}\sin(\theta(x)),.\ 
\intertext{Put $f(x) = \sin(x)$ and $g(x) = \theta(x)$. Thus}
f'(g(x))g'(x) &= \cos(\theta(x))\theta'(x).
\end{align}
So overall, you differentiated $\sin(\theta)$ with respect to $\theta$.
\end{document}