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\author{Melinluvsu}
\pdfinfo{
  /Title (algebra-ii-final.pdf)
  /Creator (Cheatography)
  /Author (Melinluvsu)
  /Subject (Algebra II Final Cheat Sheet)
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\noindent
\begin{multicols}{3}
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    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Algebra II Final Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Melinluvsu} via \textcolor{DarkBackground}{\uline{cheatography.com/21795/cs/4295/}}}
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Melinluvsu \\
  \uline{cheatography.com/melinluvsu} \\
  \end{tabulary}
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\begin{tabulary}{5.8cm}{L}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 8th June, 2015.\\
   Updated 12th May, 2016.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\end{multicols}}




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\begin{multicols*}{4}

\begin{tabularx}{3.833cm}{X}
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Periodic Functions}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{Periodic Function: repeats a pattern of y-values (outputs) at regular intervals \newline % Row Count 2 (+ 2)
Cycle: may begin at any point in a graph  \newline % Row Count 3 (+ 1)
Period: is the horizontal length of one cycle.% Row Count 4 (+ 1)
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\begin{tabularx}{3.833cm}{X}
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Special Right Angles}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{{\bf{45-45-90}} \newline % Row Count 1 (+ 1)
h = sqrt 2 times {\emph{l}} \newline % Row Count 2 (+ 1)
{\bf{30-60-90}} \newline % Row Count 3 (+ 1)
h = 2 times s \newline % Row Count 4 (+ 1)
{\emph{l}} = sqrt 3 times s% Row Count 5 (+ 1)
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Properties Of Sine Functions}}  \tn
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period = 2pi/{\emph{b}}% Row Count 2 (+ 1)
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\mymulticolumn{1}{x{3.833cm}}{|{\emph{a}}| = amplitude \newline {\emph{b}} = number of cycles (0 to 2pi)}  \tn 
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\begin{tabularx}{3.833cm}{X}
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Quadratic Functions}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{{\bf{Standard Form}} \newline % Row Count 1 (+ 1)
f(x) = ax\textasciicircum{}2\textasciicircum{} + bx + c% Row Count 2 (+ 1)
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\mymulticolumn{1}{x{3.833cm}}{ax\textasciicircum{}2\textasciicircum{} \newline Quadratic term \newline  \newline bx \newline Linear term \newline  \newline c \newline constant term}  \tn 
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\begin{tabularx}{3.833cm}{X}
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Exponential Growth \& Exponential Decay}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{b= 1 + r \newline % Row Count 1 (+ 1)
b\textgreater{}1 = epon. growth \newline % Row Count 2 (+ 1)
When b\textless{}1, b is a decay factor \newline % Row Count 3 (+ 1)
x-axis = asymptote \newline % Row Count 4 (+ 1)
0\textless{}b\textless{}1 \newline % Row Count 5 (+ 1)
b= 1+(-r) \newline % Row Count 6 (+ 1)
y=ab\textasciicircum{}x\textasciicircum{}% Row Count 7 (+ 1)
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\mymulticolumn{1}{x{3.833cm}}{b= growth factor \newline r= increase in rate}  \tn 
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{{\emph{e}} {\bf{\& Its Importance}}}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{radian 2pi, tangent 0 \newline radian pi/6, tangent sqrt 3/3 \newline radian pi/4, tangent 1 \newline radian pi/3, tangent sqrt 3 \newline radian pi/2, tangent undefined \newline radian 2pi/3, tangent -sqrt 3 \newline radian 3pi/4, tangent -1 \newline radian 5pi/6, tangent -sqrt3/3 \newline radian pi, tangent 0 \newline radian 7pi/6, tangent sqrt3/3 \newline radian 5pi/4, tangent 1 \newline radian 4pi/3, tangent sqrt3 \newline radian 3pi/2, tangent undefined \newline radian 5pi/3, tangent -sqrt3 \newline radian 7pi/4, tangent -1 \newline radian 11pi/6, tangent sqrt3/3}  \tn 
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\mymulticolumn{1}{x{3.833cm}}{{\bf{Reciprocal Identities}} \newline % Row Count 1 (+ 1)
csc theta = 1/sin theta \newline % Row Count 2 (+ 1)
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{\bf{Pythagorean Identities}} \newline % Row Count 8 (+ 1)
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{\bf{Angle Sum Identities}} \newline % Row Count 5 (+ 1)
sin (A+B) = sinA cosB + cosA SinB \newline % Row Count 6 (+ 1)
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\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{{\bf{Double-Angle Identities}} \newline % Row Count 1 (+ 1)
cos2 x = cos\textasciicircum{}2\textasciicircum{} x- sin\textasciicircum{}2\textasciicircum{} x \newline % Row Count 2 (+ 1)
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{\bf{Half Angle Identities}} \newline % Row Count 7 (+ 1)
sin A/2 = +/- sqrt 1-cosA/2 \newline % Row Count 8 (+ 1)
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\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Logarithms}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{- to base b of a positive number y is defined as... \newline % Row Count 2 (+ 2)
If y=ab\textasciicircum{}x\textasciicircum{}, then logb y= x \newline % Row Count 3 (+ 1)
{\bf{Log In Life}} \newline % Row Count 4 (+ 1)
pH= -log{[}H\textasciicircum{}+\textasciicircum{}{]}% Row Count 5 (+ 1)
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\mymulticolumn{1}{x{3.833cm}}{{\bf{b is not equal to 1}} \newline {\bf{b must be positive}} \newline {\bf{log of 0 or negative number = undefined}} \newline  \newline log= log base 10}  \tn 
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\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Log Are Inverses Of Exponentials}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{1. Graph exponenetial function \newline % Row Count 1 (+ 1)
2. Graph y = x \newline % Row Count 2 (+ 1)
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\begin{tabularx}{3.833cm}{X}
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Properties Of Log}}  \tn
\SetRowColor{white}
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logb M\textasciicircum{}x\textasciicircum{} = x logb M  \textless{}-{}-{}-{}-Power property% Row Count 4 (+ 1)
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\mymulticolumn{1}{x{3.833cm}}{{\bf{WATCH OUT FOR ERRORS}} \newline logb a/logb c does not equal logb a/c \newline  \newline logb a times c does not equal logb a times logb c}  \tn 
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\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Expanding Log}}  \tn
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\mymulticolumn{1}{x{3.833cm}}{left to right = expand \newline  \newline right to left = simplify}  \tn 
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\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Natural Log}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Write 3ln6 - ln8 as a single natural log \newline % Row Count 1 (+ 1)
ln 6\textasciicircum{}3\textasciicircum{}/8 -{}-{}-\textgreater{} ln 216/8 -{}-{}-\textgreater{} ln 27% Row Count 2 (+ 1)
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\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Solving Log Equations}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{Pt 1 \newline % Row Count 1 (+ 1)
solve log(3x+1) = 5 \newline % Row Count 2 (+ 1)
3x+1 = 10\textasciicircum{}5\textasciicircum{} \newline % Row Count 3 (+ 1)
3x+1 = 100000 \newline % Row Count 4 (+ 1)
3x = 99,999 \newline % Row Count 5 (+ 1)
x = 33,333 \newline % Row Count 6 (+ 1)
Pt 2 \newline % Row Count 7 (+ 1)
Solve 2log x- log 3 = 2 \newline % Row Count 8 (+ 1)
log(x\textasciicircum{}2\textasciicircum{}/3)=2 \newline % Row Count 9 (+ 1)
x\textasciicircum{}2\textasciicircum{}/3 = 10\textasciicircum{}2 \newline % Row Count 10 (+ 1)
x\textasciicircum{}2\textasciicircum{}= 2(100) \newline % Row Count 11 (+ 1)
x=10sqrt3 or 17.32% Row Count 12 (+ 1)
} \tn 
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\par\addvspace{1.3em}

\begin{tabularx}{3.833cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Pairs Of Relations are Inverse Of Each Other}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{3.833cm}}{y = x - 7/2 \newline % Row Count 1 (+ 1)
y = 2x+7 \newline % Row Count 2 (+ 1)
y = 3x - 1 \newline % Row Count 3 (+ 1)
y = x +1/3 \newline % Row Count 4 (+ 1)
y = -x + 4 \newline % Row Count 5 (+ 1)
y = -x + 4/-1 \newline % Row Count 6 (+ 1)
y = x + 4/5 \newline % Row Count 7 (+ 1)
y = 5x - 4% Row Count 8 (+ 1)
} \tn 
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\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}