The NumPy arccos() function is the trigonometric inverse cosine function so that, if y = cos(x), then x = arccos(y). If you apply it to a NumPy array, it performs the function element-wise.
numpy.arccos(x, out=None, where=True, <optional keyword arguments>)
| Arguments | Type | Description |
|---|---|---|
| x | array_like | x-coordinate on the unit circle. For real arguments, the domain is [-1, 1]. |
| 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 out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized 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. |
The following table shows the return value of the function:
| Return Value | Type | Description |
|---|---|---|
| angle | ndarray | The angle of the ray intersecting the unit circle at the given x-coordinate in radians [0, pi]. This is a scalar if x is a scalar. |
Related: cos, arctan, arcsin, emath.arccos
Notes
arccos is a multivalued function: for each x there are infinitely many numbers z such that cos(z) = x. The convention is to return the angle z whose real part lies in [0, pi].
For real-valued input data types, arccos 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, arccos is a complex analytic function that has branch cuts [-inf, -1] and [1, inf] and is continuous from above on the former and from below on the latter.
The inverse cos is also known as acos or cos^-1.
Let’s dive into some examples to show how the function is used in practice:
Examples
Any master coder has a “hands-on” mentality with a bias towards action. Try it yourself—play with the function in the following interactive code shell:
Exercise: Modify the linspace() function so that you plot the arccos from -100 to +100!
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