Difference: DiagnosticTest (9 vs. 10)

Revision 102007-04-10 - DickFurnas

Line: 1 to 1
 

Diagnostic Tests:

Welcome to the Math Support Center!
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Link to: MathTest for example MathMode syntax. 

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What further explanation could you possibly want here??? 

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Table of Contents
Error during latex2img:
ERROR: problems during latex
INPUT:
\documentclass[fleqn,12pt]{article}
\usepackage{amsmath}
\usepackage[normal]{xcolor}
\setlength{\mathindent}{0cm}
\definecolor{teal}{rgb}{0,0.5,0.5}
\definecolor{navy}{rgb}{0,0,0.5}
\definecolor{aqua}{rgb}{0,1,1}
\definecolor{lime}{rgb}{0,1,0}
\definecolor{maroon}{rgb}{0.5,0,0}
\definecolor{silver}{gray}{0.75}
\usepackage{latexsym}
\begin{document}
\pagestyle{empty}
\pagecolor{white}
{
\color{black}
\begin{math}\displaystyle = \frac{\Pi}{6} radians\end{math}
}
\clearpage
{
\color{black}
\begin{math}\displaystyle = \frac{60\Pi}{360} radians\end{math}
}
\clearpage
{
\color{black}
\begin{math}\displaystyle 30^{\circ} \dot $\frac{ 2\Pi radians }{ 360^{\circ}$ }\end{math}
}
\clearpage
{
\color{black}
\begin{math}\displaystyle = 2\Pi radians\end{math}
}
\clearpage
{
\color{black}
\begin{math}\displaystyle \frac{\Pi}{6}\end{math}
}
\clearpage
{
\color{black}
\begin{math}\displaystyle = 360^{\circ}\end{math}
}
\clearpage
\end{document}
STDERR:
This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013)
 restricted \write18 enabled.
entering extended mode
(/tmp/Fsd55fjzWK/8OYt6uQkV_
LaTeX2e <2011/06/27>
Babel  and hyphenation patterns for english, dumylang, nohyphenation, lo
aded.
(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/fleqn.clo)
(/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the `?' option.
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty))
(/usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/graphics/dvips.def))
(/usr/share/texlive/texmf-dist/tex/latex/base/latexsym.sty)
No file 8OYt6uQkV_.aux.
(/usr/share/texlive/texmf-dist/tex/latex/base/ulasy.fd) [1] [2]
! Extra }, or forgotten $.
 }
                 
l.27 \begin{math}\displaystyle 30^{\circ} \dot $
                                                \frac{ 2\Pi radians }{ 360^{...

! Missing } inserted.
 
                }
l.27 \begin{math}\displaystyle 30^{\circ} \dot $
                                                \frac{ 2\Pi radians }{ 360^{...

! Missing } inserted.
 
                }
l.27 ...dot $\frac{ 2\Pi radians }{ 360^{\circ}$ }
                                                  \end{math}
! Extra }, or forgotten \endgroup.
\frac  #1#2->{\begingroup #1\endgroup \@@over #2}
                                                 
l.27 ...dot $\frac{ 2\Pi radians }{ 360^{\circ}$ }
                                                  \end{math}

! LaTeX Error: Bad math environment delimiter.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H   for immediate help.
 ...                                              
                                                  
l.27 ...{ 2\Pi radians }{ 360^{\circ}$ }\end{math}
                                                  
[3] [4] [5] [6] (./8OYt6uQkV_.aux) )
(see the transcript file for additional information)
Output written on 8OYt6uQkV_.dvi (6 pages, 1772 bytes).
Transcript written on 8OYt6uQkV_.log.
Line: 13 to 28
  Combine and simplify expressions as much as possible.
Solve equations for x.
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  • Cannot be simplified.
  • however, if we are told further that then we have a common factor in the denominator:
    • , provided 

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  • No algebraic simplification.
  • however... A beautiful geometric simplification is possible:
    • is the hypotenuse of the right triangle with sides and 

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Alternatively:

Recall Pascal's Triangle: 

                1    1
             1    2    1
          1    3    3    1
       1    4     6    4     1
    1    5   10   10    5    1

...in which elements in a row are the sum of the two elements in the row above it. These numbers are the Binomial Coefficients. is the cube of the binomial so the coefficients can be taken from the third row above: 1  3  3  1 and the exponents on start with and count down, while the exponents on start with and count up:

which simplifies to:

as previously. 

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if a product is zero one of its factors must be zero so:

either or or

and either or or 

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  • Rearrange so the equation is of the form:
  • and use the Quadratic Formula: 
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Trig

Answer the following questions without calculators or trig tables.
Leave answers like or as is.
Changed:
<
<
  1. Convert:
    1. to radians.
    2. to degrees.
    3. to radians.
  2. Evaluate:
  3. Sketch the graph of
>
>

1. Convert:

a. to radians.

b. to degrees.

c. to radians.

2. Evaluate:

a.

b.

c.

3. Sketch the graph of

  (Make your vertical scale as large as possible.)
Changed:
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<
  1. Given
  2. Solve the following right triangle:
>
>

4. Given

5. Solve the following right triangle:

  ( i.e. determine missing sides and angles.)
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  2. Relate to and
    2. %#$\mbox{ \small $\sin{\frac{\pi}{2} -\theta}$ }$%
    3. %#$\mbox{ \small $\sin{2\theta}$ }$%
  3. Express in terms of of
>
>

a.

b.

c.

6. Relate to and

a.

b.

c.

7. Express in terms of and of and :

 
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