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

\usepackage[linguistics]{forest}

\begin{document}

	\maketitle
		{Warm-Up: Exact answers}
		{Prepared by Mark on \today.}

	\vspace{2mm}

	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 idenity 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 geometery and the identities above.
	\end{solution}

\end{document}