Practical Considerations
For angles near 0 and π, arccosine is ill-conditioned and will thus calculate the angle with reduced accuracy in a computer implementation (due to the limited number of digits). Similarly, arcsine is inaccurate for angles near −π/2 and π/2. To achieve full accuracy for all angles, arctangent or atan2 should be used for the implementation.
Read more about this topic: Inverse Trigonometric Functions
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“Consider what effects which might conceivably have practical bearings we conceive the object of our conception to have. Then our conception of these effects is the whole of our conception of the object.”
—Charles Sanders Peirce (1839–1914)