38 lines
1006 B
TeX
Executable File
38 lines
1006 B
TeX
Executable File
\documentclass[
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solutions,
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nowarning,
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singlenumbering,
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nopagenumber
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]{../../resources/ormc_handout}
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\usepackage[linguistics]{forest}
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\begin{document}
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\maketitle
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{Warm-Up: Exact answers}
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{Prepared by Mark on \today.}
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\vspace{2mm}
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Compute the exact value of $\sin(x^\circ)$ for as many integers $x \in [0, 90]$ as you can.
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\generic{Helpful identities:}
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This is not a complete list. In many cases, geometry is more helpful than algebra. \\
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Note that the first idenity is only valid if $\alpha \in [0, 90]$.
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\vspace{2mm}
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$\sin(\frac{\alpha}{2}) = \sqrt{\frac{1 - \cos(\alpha)}{2}}$ \\
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$\sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta)$ \\
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$\sin(3\alpha) = 3\sin(\alpha) - 4\sin(\alpha)^3$
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\begin{solution}
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The solutions to these get ugly quickly.
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\vspace{5mm}
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A good order to go in is 45, 30, 60, 15, 75, 36, 18, 3, 6, 72, 9, 1. \\
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You should be able to get all of these using only geometery and the identities above.
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\end{solution}
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\end{document} |