Inverse Trigonometric Functions

Defines the domain and principal value branch (range) of the inverse sine function.

Defines the domain and principal value branch (range) of the inverse cosine function.

Defines the domain and principal value branch (range) of the inverse tangent function.

Defines the domain and principal value branch (range) of the inverse cotangent function.

Defines the domain and principal value branch (range) of the inverse secant function.

Defines the domain and principal value branch (range) of the inverse cosecant function.

Evaluates the inverse sine of sine when the angle lies in the principal value interval.

Evaluates the inverse cosine of cosine when the angle lies in the principal value interval.

Evaluates the inverse tangent of tangent when the angle lies in the principal value interval.

Gives the sign-reversal rule for evaluating odd inverse trigonometric functions at negative arguments.

Gives the π-shift reflection identity for evaluating inverse cosine, cotangent, and secant at negative inputs.

Expresses inverse cotangent in terms of inverse tangent, accounting for the π shift when x is negative.

Converts inverse cosecant and inverse secant to inverse sine and cosine respectively.

States that the sum of any co-function pair of inverse trigonometric functions equals π/2 on their common domain.

Combines two inverse tangents into one when the product xy is strictly less than 1.

Computes the difference between two inverse tangents when xy is strictly greater than -1.

Expresses twice an inverse tangent as a single inverse tangent for |x| < 1.

Transforms twice an inverse tangent into an inverse sine for |x| <= 1.

Transforms twice an inverse tangent into an inverse cosine for non-negative x.