\documentclass[
	solutions,
	singlenumbering,
	nopagenumber
]{../../resources/ormc_handout}

\usepackage[linguistics]{forest}


\title{Warm-Up: Exact answers}
\subtitle{Prepared by Mark on \today}

\begin{document}

	\maketitle

	Compute the exact value of $\sin(x^\circ)$ for as many integers $x \in [0, 90]$ as you can.

	\generic{Helpful identities:}
	This is not a complete list. In many cases, geometry is more helpful than algebra. \\
	Note that the first identity is only valid if $\alpha \in [0, 90]$.

	\vspace{2mm}
	$\sin(\frac{\alpha}{2}) = \sqrt{\frac{1 - \cos(\alpha)}{2}}$ \\
	$\sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta)$ \\
	$\sin(3\alpha) = 3\sin(\alpha) - 4\sin(\alpha)^3$

	\begin{solution}
		The solutions to these get ugly quickly.

		\vspace{5mm}

		A good order to go in is 45, 30, 60, 15, 75, 36, 18, 3, 6, 72, 9, 1. \\
		You should be able to get all of these using only geometry and the identities above.
	\end{solution}

\end{document}