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# Mathematical

The following functions are supported by the Synthetic Variables Mathematical Expressions. These functions receive a variable's time series data as its arguments.
Syntax
Description
$ceil(x)$
Returns the rounded integer greater or equal for each element in the variable x. The ceil function always rounds up to the nearest integer.
$round(x, n)$
Returns the floating-point value rounded to the n digits after the decimal point for each element in the variable x. By default, n equals 2 in Ubidots.
$sin(x)$
Returns the sine in radians of each element in the variable x.
$cos(x)$
Returns the cosine in radians of each element in the variable x.
$tan(x)$
Returns the tangent of each element in the variable x.
$arcsin(x)$
Returns in radians the inverse sine of each element in the variable x.
$arccos(x)$
Returns in radians the inverse sine of each element in the variable x.
$arctan(x)$
Returns in radians the inverse tangent of each element in the variable x.
$arctan2(x, y)$
Returns in radians the trigonometric inverse tangent using the input variables x and y as Cartesian coordinates. Note: It will only perform the operation between values with the same timestamp.
$sinh(x)$
Returns the hyperbolic sine of each element in the variable x.
$cosh(x)$
Returns the hyperbolic cosine of each element in the variable x.
$tanh(x)$
Returns the hyperbolic tangent of each element in the variable x.
$arcsinh(x)$
Returns in radians the inverse hyperbolic sine of each element in the variable x.
$arccosh(x)$
Returns in radians the inverse hyperbolic cosine of each element in the variable x.
$arctanh(x)$
Returns in radians the inverse hyperbolic tangent of each element in the variable x.
$exp(x)$
Returns the exponential of each element in the variable x.
$log(x, base)$
Returns the logarithm of each element in the variable x. By default, the base is the Euler's number.
$abs(x)$
Returns the absolute value of each element in the variable x.
$sqrt(x)$
Returns the square root value of each element in the variable x.
xandyrepresent variables as time series or dots