ATAN

Purpose:

Calculates the inverse tangent of any expression.

Syntax:

ATAN(val)

val

-

A scalar, series or table.

Returns:

A scalar, series, or table.

Example:

atan(-12..0.01..12);gridhv;griddot

 

 

image\atanpic01.gif

 

displays the inverse tangent from 12 to 12.

Example:

atan(1)

 

returns 0.78539816, or π/4.

Example:

atan(inf)

 

returns 1.570796, or π/2.

Example:

atan(-2..0.1..2)

 

returns a 41 point series.

Remarks:

The inverse tangent is defined as:

 

image\atan01.gif

 

for all complex z. The function is multi-valued and this definition places the branch cut in the complex plane at [-i ∞, -i] and [i, i ∞].

 

image\atan02.gif

 

For real x,

 

/2  ≤  atan(x)  ≤  π/2

 

Using atan(imag(x)/real(x)) to calculate the phase angle of a complex scalar or series x will not distinguish between numbers in quadrants I and III, or between numbers in quadrants II and IV. See PHASE

 

See ATAN2 for a 4 quadrant implementation of the inverse tangent function.

 

The function calculates in radians unless degrees are specified with the SETDEGREE function.

See Also:

ANGLE

ACOT

ATAN2

ATANH

GATAN

PHASE

SETDEGREE

SETRADIAN

TAN

TANH

TRIGONOMETRIC FUNCTIONS