diff --git a/Misc/Warm-Ups/sin.tex b/Misc/Warm-Ups/sin.tex new file mode 100755 index 0000000..d6fcf8a --- /dev/null +++ b/Misc/Warm-Ups/sin.tex @@ -0,0 +1,38 @@ +\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} \ No newline at end of file