37 lines
1016 B
TeX
Executable File
37 lines
1016 B
TeX
Executable File
\documentclass[
|
|
solutions,
|
|
singlenumbering,
|
|
nopagenumber
|
|
]{../../resources/ormc_handout}
|
|
\usepackage{../../resources/macros}
|
|
|
|
|
|
\title{Warm-Up: Exact answers}
|
|
\uptitler{\smallurl{}}
|
|
\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} |