% [INTRO_OCTAVE_02.tex] <[FORM_INTRO_OCTAVE.tex] 2014.06.29
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                 {\running \ifnum \pageno > 5 Section 02: Common functions
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\centerline{\bfsixteen Section 02: Common functions}   %  title of section
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\centerline{\bf Trigonometric functions}
\mni
{\bf sin({\tt a})},   {\bf cos({\tt a})},   {\bf tan({\tt a})}.\q [{\tt a} is 
measured in radians, multiply by ${180}\over{\pi}$ for degrees]
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\centerline{\bf Logarithmic functions}
\mni
%\pni
The ``natural logarithm'', usually written ln({\tt a}): {\bf log({\tt 
a})}
\pni
The logarithm to the base 10: {\bf log10({\tt a})}
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 \centerline{\bf pi,   e,  complex numbers}
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 \sni
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 {\bf pi}
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 \sni
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{\bf e}:  the base of the ``natural logarithm''
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\sni
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{\bf i}:  $\sqrt{-1}$
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%    FORM FOR OUTPUT	
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{\tt  %  for programs
\obeylines
\parindent = 0pt
\parskip =  -1.0 pt  %was-2.5pt THIS LEAVES MORE SPACE
octave:1> {\bf pi}
\qq\q ans =  3.1416
\%
\%\qq e, the base of the ``natural logarithm''
octave:1>{\bf  e}  
\qq\q ans =  2.7183
\%
\%\qq   always use {\bf (\en )}, even when not strictly necessary
octave:2> (e){\bf \^{}}(2)
\qq\q ans =  7.3891
\%
\%\qq square root of a negative number
octave:3> {\bf sqrt(}-5{\bf)}
\qq\q ans =  0.00000 + 2.23607i
\%
\%\qq  cube of a complex number
octave:5> (2 -5i){\bf\^{}}(3)
\qq\q ans = -142 +  65i
} % end \tt  %  for programs
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\centerline{\bf Displaying the answer}
\mni
Octave stores values to a very high degree of accuracy. If you 
want to see the answer to
15 places, use {\bf format long}.
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{\tt  %  for programs
\obeylines
\parindent = 0pt
\parskip =  -1.0 pt  %was-2.5pt THIS LEAVES MORE usually writtenSPACE
octave:3> format long
octave:4> pi
\qq\q ans =  3.14159265358979
%
} % end \tt  %  for programs
\mni
To show your answer in ``scientific'' (``floating point'') notation use:\pni
{\bf format short e}\pni
\qq or\pni
{\bf format long e}
\sni
To show the answer to 2 decimal places,  use:\pni
{\bf format bank} [money in dollars and cents is shown to 2 decimal places]
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{\tt  %  for programs
\obeylines
\parindent = 0pt
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octave:6> format short e
octave:7> 1/7
\qq\q ans =  1.4286e-01
\%
octave:8> format long e
octave:9> 1/7
\qq\q ans =  1.42857142857143e-01
\%
octave:10> format bank
octave:11> 1/7
\qq\q ans = 0.14
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} % end \tt  %  for programs
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\centerline{\bf Absolute value,  rounding the answer etc.}
\mni
 absolute value: {\bf abs}\gl({\tt a})\pni
 round to the nearest integer: {\bf round}\gl({\tt a})\pni
 round downwards:         {\bf floor}\gl({\tt a})\q [=\th ``greatest integer function'']\pni
 round upwards:           {\bf ceil}\gl({\tt a})\pni
 round towards 0 :              {\bf fix}({\tt a})\pni
% sign function:  {\bf sign}({\tt a}). This takes on the values 
% 1,0,-1 %depending on whether {\tt a}> 0,
% {\tt a}=0,  {\tt a} < 0\th.\pni       
\sni
The following function is not built-in;
we will create  it in the next section.
\pni
 \bibl decimal part: {\bf decimal}( ) 
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\bni
Octave has  many more built-in functions, and we will see some of these when we talk about vectors 
and matrices.
\bni
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\centerline{\bf Try these}
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\sni
\item{1.} Find $\log_{10}\Bigl({10\,}^{271.6}\Bigr)$.
\sni
\item{2.} Compute ${10\,}^{0.5}$. Compare the answer with the Octave square root 
command:
{\bf sqrt}(10).
\sni
\item{3.} Evaluate the numbers  2.71 and -2.71, first  using the
definitions of {\bf abs}, {\bf round}, {\bf floor},
 {\bf ceil}, {\bf fix} and {\bf sign} and then by using Octave.
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