Inverse Trigonometric Functions The definitions of the inverse functions for secant, cosecant, and cotangent will be similar to the development for the inverse functions for sine, cosine, and tangent. Each of these functions fail to pass the horizontal line test, so they are not 1-1 and none of them have inverses on their normal domains.

We must restrict the domain of the cosecant function so that it will be a 1-1 function, and have an inverse. This could be done in several ways, but the following is most common:

Definition: Inverse Cosecant

Another way of writing the inverse of the cosecant function is as follows:

We must restrict the domain of the secant function so that it will be a 1-1 function, and have an inverse. This could be done in several ways, but the following is most common:

Definition: Inverse Secant

Another way of writing the inverse of the secant function is as follows:

We must restrict the domain of the cotangent function so that it will be a 1-1 function, and have an inverse. This could be done in several ways, but the following is most common:

Definition: Inverse Cotangent

Another way of writing the inverse of the cotangent function is as follows: