numpy.arctan(x[, out])

Trigonometric inverse tangent, element-wise.

The inverse of tan, so that if y = tan(x) then x = arctan(y).


x : array_like

Input values. arctan is applied to each element of x.


out : ndarray

Out has the same shape as x. Its real part is in [-pi/2, pi/2]. It is a scalar if x is a scalar.

See also

Calculate the arctan of y/x.


arctan is a multivalued function: for each x there are infinitely many numbers z such that tan(z) = x. The convention is to return the angle z whose real part lies in [-pi/2, pi/2].

For real-valued input data types, arctan always returns real output. For each value that cannot be expressed as a real number or infinity, it yields nan and sets the invalid floating point error flag.

For complex-valued input, arctan is a complex analytical function that has branch cuts [1j, infj] and [-1j, -infj] and is continuous from the left on the former and from the right on the latter.

The inverse tangent is also known as atan or tan^-1.


[R10]M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 79.
[R11]Wikipedia, “Inverse trigonometric function”,


We expect the arctan of 0 to be 0, and of 1 to be \pi/4:

>>> np.arctan([0, 1])
array([ 0.        ,  0.78539816])
>>> np.pi/4

Plot arctan:

>>> import matplotlib.pyplot as plt
>>> x = np.linspace(-10, 10)
>>> plt.plot(x, np.arctan(x))
>>> plt.axis('tight')

(Source code)



(png, pdf)

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