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#### 10.7.14 Maths

Standard mathematical and trigonometric functions. Trigonometric functions work with angles in radians.

`sin( theta )`
Sine of an angle.

• Parameters:
• `theta` (floating point): an angle, in radians.
• Return value
• (floating point): the sine of the argument.

`cos( theta )`
Cosine of an angle.

• Parameters:
• `theta` (floating point): an angle, in radians.
• Return value
• (floating point): the cosine of the argument.

`tan( theta )`
Tangent of an angle.

• Parameters:
• `theta` (floating point): an angle, in radians.
• Return value
• (floating point): the tangent of the argument.

`asin( x )`
Arc sine of an angle. The result is in the range of -pi/2 through pi/2.

• Parameters:
• `x` (floating point): the value whose arc sine is to be returned.
• Return value
• (floating point): the arc sine of the argument (radians)

`acos( x )`
Arc cosine of an angle. The result is in the range of 0.0 through pi.

• Parameters:
• `x` (floating point): the value whose arc cosine is to be returned.
• Return value
• (floating point): the arc cosine of the argument (radians)

`atan( x )`
Arc tangent of an angle. The result is in the range of -pi/2 through pi/2.

• Parameters:
• `x` (floating point): the value whose arc tangent is to be returned.
• Return value
• (floating point): the arc tangent of the argument (radians)

`ln( x )`
Natural logarithm.

• Parameters:
• `x` (floating point): argument
• Return value
• (floating point): loge(x)

`exp( x )`
Euler's number e raised to a power.

• Parameters:
• `x` (floating point): the exponent to raise e to.
• Return value
• (floating point): the value ex, where e is the base of the natural logarithms.

`log10( x )`
Logarithm to base 10.

• Parameters:
• `x` (floating point): argument
• Return value
• (floating point): log10(x)

`exp10( x )`
Power of 10. This convenience function is identical to `pow(10,x)`.

• Parameters:
• `x` (floating point): argument
• Return value
• (floating point): 10x

`sqrt( x )`
Square root. The result is correctly rounded and positive.

• Parameters:
• `x` (floating point): a value.
• Return value
• (floating point): the positive square root of `x`. If the argument is NaN or less than zero, the result is NaN.

`square( x )`
Raise to the power 2.

• Parameters:
• `x` (floating point): a value
• Return value
• (floating point): x * x

`hypot( xs, ... )`
Returns the square root of the sum of squares of its arguments. In the 2-argument case, doing it like this may avoid intermediate overflow or underflow.

• Parameters:
• `xs` (floating point, one or more): one or more numeric values
• Return value
• (floating point): sqare root of sum of squares of arguments
• Examples:
• `hypot(3,4) = 5`
• `hypot(2,2,2,2) = 4`

`atan2( y, x )`
Converts rectangular coordinates (`x`,`y`) to polar (`r`,`theta`). This method computes the phase `theta` by computing an arc tangent of `y/x` in the range of -pi to pi.

• Parameters:
• `y` (floating point): the ordinate coordinate
• `x` (floating point): the abscissa coordinate
• Return value
• (floating point): the `theta` component (radians) of the point (`r`,`theta`) in polar coordinates that corresponds to the point (`x`,`y`) in Cartesian coordinates.

`pow( a, b )`
Exponentiation. The result is the value of the first argument raised to the power of the second argument.

• Parameters:
• `a` (floating point): the base.
• `b` (floating point): the exponent.
• Return value
• (floating point): the value `ab`.

`sinh( x )`
Hyperbolic sine.

• Parameters:
• `x` (floating point): parameter
• Return value
• (floating point): result

`cosh( x )`
Hyperbolic cosine.

• Parameters:
• `x` (floating point): parameter
• Return value
• (floating point): result

`tanh( x )`
Hyperbolic tangent.

• Parameters:
• `x` (floating point): parameter
• Return value
• (floating point): result

`asinh( x )`
Inverse hyperbolic sine.

• Parameters:
• `x` (floating point): parameter
• Return value
• (floating point): result

`acosh( x )`
Inverse hyperbolic cosine.

• Parameters:
• `x` (floating point): parameter
• Return value
• (floating point): result

`atanh( x )`
Inverse hyperbolic tangent.

• Parameters:
• `x` (floating point): parameter
• Return value
• (floating point): result

`E`
Euler's number e, the base of natural logarithms.

`PI`
Pi, the ratio of the circumference of a circle to its diameter.

`Infinity`
Positive infinite floating point value.

`NaN`
Not-a-Number floating point value. Use with care; arithmetic and logical operations behave in strange ways near NaN (for instance, `NaN!=NaN`). For most purposes this is equivalent to the blank value.

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STILTS - Starlink Tables Infrastructure Library Tool Set
Starlink User Note256
STILTS web page: http://www.starlink.ac.uk/stilts/
Author email: m.b.taylor@bristol.ac.uk
Mailing list: topcat-user@jiscmail.ac.uk