In Exercises 83–94, use a right triangle to write each expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x.csc (cot⁻¹ x)

Inverse trigonometric functions, such as cot⁻¹(x), are used to find angles when the value of a trigonometric function is known. For example, cot⁻¹(x) gives the angle whose cotangent is x. Understanding how to interpret these functions is crucial for solving problems involving right triangles.

The cosecant function, denoted as csc(θ), is the reciprocal of the sine function, defined as csc(θ) = 1/sin(θ). In the context of a right triangle, it relates the length of the hypotenuse to the length of the opposite side. Recognizing how to express csc in terms of other trigonometric functions is essential for simplifying expressions.

In a right triangle, the relationships between the angles and sides are governed by trigonometric ratios. The sides are typically labeled as opposite, adjacent, and hypotenuse, which correspond to the angles. Understanding these relationships allows for the conversion of trigonometric expressions into algebraic forms, facilitating the solution of problems involving angles and side lengths.