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arctan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

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

Notes

arctan is a multi-valued function: for each x there are infinitely many numbers :None:None:`z` such that tan(:None:None:`z`) = x. The convention is to return the angle :None:None:`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 :None:None:`invalid` floating point error flag.

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

The inverse tangent is also known as :None:None:`atan` or tan^{-1}.

Parameters

x : array_like
out : ndarray, None, or tuple of ndarray and None, optional

A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.

where : array_like, optional

This condition is broadcast over the input. At locations where the condition is True, the :None:None:`out` array will be set to the ufunc result. Elsewhere, the :None:None:`out` array will retain its original value. Note that if an uninitialized :None:None:`out` array is created via the default out=None , locations within it where the condition is False will remain uninitialized.

**kwargs :

For other keyword-only arguments, see the ufunc docs <ufuncs.kwargs> .

Returns

out : ndarray or scalar

Out has the same shape as x. Its real part is in [-pi/2, pi/2] ( arctan(+/-inf) returns +/-pi/2 ). This is a scalar if x is a scalar.

Trigonometric inverse tangent, element-wise.

See Also

angle

Argument of complex values.

arctan2

The "four quadrant" arctan of the angle formed by (:None:None:`x`, :None:None:`y`) and the positive :None:None:`x`-axis.

Examples

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

This example is valid syntax, but we were not able to check execution
>>> np.arctan([0, 1])
array([ 0.        ,  0.78539816])
This example is valid syntax, but we were not able to check execution
>>> np.pi/4
0.78539816339744828

Plot arctan:

This example is valid syntax, but we were not able to check execution
>>> import matplotlib.pyplot as plt
... x = np.linspace(-10, 10)
... plt.plot(x, np.arctan(x))
... plt.axis('tight')
... plt.show()
See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

numpy.ma.core.arccos numpy.ma.core.arcsin numpy.ma.core.arctan2 numpy.ma.core.arctan

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