Inverse Trigonometric Functions

In mathematics, the inverse trigonometric functions (occasionally called cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions. They are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.

There are many notations used for the inverse trigonometric functions. The notations  sin⁻¹ (x), cos⁻¹ (x), tan⁻¹ (x), etc. are often used, but this convention logically conflicts with the common semantics for expressions like sin² (x), which refer to numeric power rather than function composition, and therefore may result in confusion between multiplicative inverse and compositional inverse. Another convention used by some authors[2] is to use a majuscule (capital/upper-case) first letter along with a −1 superscript, e.g., Sin⁻¹ (x), Cos⁻¹ (x), etc., which avoids confusing them with the multiplicative inverse, which should be represented by Sin⁻¹ (x), Cos⁻¹ (x), etc. Yet another convention is to use an arc- prefix, so that the confusion with the −1 superscript is resolved completely, e.g., arcsin (x), arccos (x), etc. This convention is used throughout the article. In computer programming languages the inverse trigonometric functions are usually called asin, acos, atan.