Basic Mathematical Functions in Scilab

Even if it’s capable of very complex numerical computations, Scilab can be used only as a simple or scientific calculator. The most common functions are those related to trigonometry, logarithms and basic statistics. In the table below the basic mathematical functions defined in Scilab are explained.

General functions

Mathematical function	Scilab function	Mathematical formula
square root	sqrt(x)	\[ \begin{equation*} \begin{split} \sqrt{x} \end{split} \end{equation*} \]
exponential	exp(x)	\[ \begin{equation*} \begin{split} e^x \end{split} \end{equation*} \]
natural algorithm	log(x)	\[ \begin{equation*} \begin{split} ln(x) \end{split} \end{equation*} \]
decimal logarithm	log10(x)	\[ \begin{equation*} \begin{split} log(x) \end{split} \end{equation*} \]
absolute value	abs(x)	\[ \begin{equation*} \begin{split} \left | x \right | \end{split} \end{equation*} \]

Trigonometry functions

Mathematical function	Scilab function	Mathematical formula
sine	sin(x)	\[ \begin{equation*} \begin{split} sin(x), x \hspace{2mm} in \hspace{2mm} radians \end{split} \end{equation*} \]
cosine	cos(x)	\[ \begin{equation*} \begin{split} cos(x), x \hspace{2mm} in \hspace{2mm} radians \end{split} \end{equation*} \]
tangent	tan(x)	\[ \begin{equation*} \begin{split} tg(x), x \hspace{2mm} in \hspace{2mm} radians \end{split} \end{equation*} \]
cotangent	cotg(x)	\[ \begin{equation*} \begin{split} ctg(x), x \hspace{2mm} in \hspace{2mm} radians \end{split} \end{equation*} \]
arc-sine	asin(x)	\[ \begin{equation*} \begin{split} y = arcsin(x), x = sin(y) \end{split} \end{equation*} \]
arc-cosine	acos(x)	\[ \begin{equation*} \begin{split} y = arccos(x), x = cos(y) \end{split} \end{equation*} \]
arc-tangent	atan(x)	\[ \begin{equation*} \begin{split} y = arctg(x), x = tg(y) \end{split} \end{equation*} \]
arc-cotangent	acot(x)	\[ \begin{equation*} \begin{split} y = arcctg(x), x = ctg(y) \end{split} \end{equation*} \]
hyperbolic sine	sinh(x)	\[ \begin{equation*} \begin{split} sinh(x) = \frac{e^x – e^{-x}}{2} \end{split} \end{equation*} \]
hyperbolic cosine	cosh(x)	\[ \begin{equation*} \begin{split} cosh(x) = \frac{e^{2 \cdot x} + 1}{2 \cdot e^x} \end{split} \end{equation*} \]
hyperbolic tangent	tanh(x)	\[ \begin{equation*} \begin{split} tanh(x) = \frac{e^{2 \cdot x} – 1}{e^{2 \cdot x} + 1} \end{split} \end{equation*} \]
hyperbolic cotangent	coth(x)	\[ \begin{equation*} \begin{split} coth(x) = \frac{e^{2 \cdot x} + 1}{e^{2 \cdot x} – 1} \end{split} \end{equation*} \]
sinc	sinc(x)	\[ \begin{equation*} \begin{split} sinc(x) = \frac{sin(x)}{x} \end{split} \end{equation*} \]

It is important to keep in mind that the argument for the trigonometric functions should be in radians. To transform from degrees in radians we use the following formula:

\[ \begin{equation*} \begin{split}
\alpha [rad] = \alpha [^{\circ}] \cdot \frac{\pi}{180^{\circ}}
\end{split} \end{equation*} \]

Example, the sine function of an angle of 90°:

-->sin(90 * %pi/180)
 ans =
 
 1. 
 
-->

Statistical functions

Mathematical function	Scilab function	Description
minimum	min(x)	\[ \begin{equation*} \begin{split} x = [x_1, x_2, …] \end{split} \end{equation*} \]
maximum	max(x)	\[ \begin{equation*} \begin{split} x = [x_1, x_2, …] \end{split} \end{equation*} \]
round	round(x)	\[ \begin{equation*} \begin{split} outputs \hspace{2mm} the \hspace{2mm} closest \hspace{2mm} integer \hspace{2mm} of \hspace{2mm} x \end{split} \end{equation*} \]
ceil	ceil(x)	\[ \begin{equation*} \begin{split} outputs \hspace{2mm} the \hspace{2mm} integer \hspace{2mm} part \hspace{2mm} of \hspace{2mm} x + 1 \end{split} \end{equation*} \]
floor	floor(x)	\[ \begin{equation*} \begin{split} outputs \hspace{2mm} the \hspace{2mm} integer \hspace{2mm} part \hspace{2mm} of \hspace{2mm} x \end{split} \end{equation*} \]

Example:

-->min([1 2 3]) + max([-2 0 1]) + round(0.6) + ceil(0.1) + floor(1.9)
 ans =
 
 5. 
 
-->

In order to get used to Scilab basic functions try the examples below:

\[ \begin{equation*} \begin{split}
e^2 + \left ( \frac{\pi}{3}\right)^3 + ln(7) – log_{10} 5 + \sqrt{18^4}
\end{split} \end{equation*} \]

-->exp(2)+(%pi/2)^3+log(7)-log10(5)+sqrt(18^4)

ans =

336.51178

-->

\[ \begin{equation*} \begin{split}
sinc(x) + tan(x)^3 – 5 \cdot \frac{ctg(x)}{arccos(x)} – cosh(x), \hspace{2mm} x = \frac{\pi}{5}
\end{split} \end{equation*} \]

-->x=%pi/5

x = 
 0.6283185 
 
-->sinc(x)+tan(x)^3-5*(cotg(x)/acos(x))-cosh(x)

ans = 
 - 7.60525 
 
-->

The best way to get use with the Scilab basic functions syntax, is to try a couple of mathematical expressions which should include basic, trigonometry and statistical functions. After some practice names and arguments of the functions will be easy to remember and use.

For any questions, observations and queries regarding Scilab variables use the comment form below.

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