atan2 atan

atan2 definition

In terms of the standard arctan function, whose range is (?π/2,
π/2), it can be expressed as follows:

0 \\ \arctan\left(\frac y x\right) + \pi& \qquad y \ge 0 , x 0 , x = 0 \\ -\frac{\pi}{2} & \qquad y

Notes:

• This produces results in the range (?π,
  π], which can be mapped to [0,
  2π) by adding 2π to
  negative results.

• Traditionally, atan2(0, 0) is
  undefined.
  
  • The C function atan2, and most other computer
    implementations, are designed to reduce the effort of transforming
    cartesian to polar coordinates and so always
    define atan2(0, 0). On implementations without signed
    zero, or when given positive zero arguments, it is normally defined as
    0. It will always return a value in the range [?π, π] rather than raising an error or
    returning a NaN (Not a Number).
  
  
  • Systems supporting symbolic mathematics normally return an undefined
    value for atan2(0,0) or otherwise signal that an
    abnormal condition has arisen.

• For systems implementing signed
  zero, infinities,
  or Not
  a Number (for example, IEEE
  floating point), it is common to implement reasonable extensions which
  may extend the range of values produced to include ?π and ?0. These also may return NaN or raise an
  exception when given a NaN argument.

• For systems implementing signed
  zero (for example, IEEE
  floating point), atan2(-0, x), x < 0 returns the value ?π. atan2(+0,
  x), x < 0 still returns +π.

atan

interval is
(-pi/2,pi/2)

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