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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—Ralph Waldo Emerson (1803–1882)