The inverse of the tangent restricted to , taking real values in that interval. Its derivative is . A formula involving an inverse tangent of a ratio may need a continuous branch of a multivalued function to describe a smooth field through a pole of that ratio.
The inverse sine is one member of the inverse trigonometric functions.
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Inverse trigonometric functions are the inverse operations of the standard trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent). These functions are used to determine the angle that corresponds to a given value of a trigonometric function. The main inverse trigonometric functions include: 1. **Arc sine (arcsin or sin⁻¹)**: The inverse of the sine function. It returns the angle whose sine is a given value.