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Aide de Scilab >> Fonctions Elémentaires > Trigonométrie > atan

atan

2-quadrant and 4-quadrant inverse tangent

Calling Sequence

phi = atan(x)
phi = atan(y, x)

Arguments

x

a real or complex scalar, vector or matrix.

phi

a real or complex scalar, vector or matrix.

x, y

a real scalars, vectors or matrices of the same size.

phi

a real scalar, vector or matrix.

Description

The first form computes the 2-quadrant inverse tangent, which is the inverse of tan(phi). For real x, phi is in the interval . For complex x, atan has two singular, branching points +%i, -%i and the chosen branch cuts are the two imaginary half-straight lines and .

The second form computes the 4-quadrant arctangent (atan2 in Fortran), this is, it returns the argument (angle) of the complex number x+i*y. The range of atan(y, x) is .

For real arguments, both forms yield identical values if x>0.

In case of vector or matrix arguments, the evaluation is done element-wise, so that phi is a vector or matrix of the same size with phi(i, j) = atan(x(i, j)) or phi(i,j) = atan(y(i, j), x(i, j)).

Examples

// examples with the second form
x=[1,%i,-1,%i]
phase_x=atan(imag(x),real(x))
atan(0,-1)
atan(-%eps,-1)

// branch cuts
atan(-%eps + 2*%i)
atan(+%eps + 2*%i)
atan(-%eps - 2*%i)
atan(+%eps - 2*%i)

// values at the branching points
ieee(2)
atan(%i)
atan(-%i)

See Also

  • tan — tangente
  • unwrap — unwrap a Y(x) profile or a Z(x,y) surface. Unfold a Y(x) profile
  • ieee — détermine le mode d'exception IEEE pour les calculs
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Last updated:
Thu Oct 02 13:54:30 CEST 2014