For each expression in Column I, choose the expression from Column II that completes an identity.
2. csc x = ____

Key Concepts

Cosecant Function

The cosecant function, denoted as csc(x), is the reciprocal of the sine function. It is defined as csc(x) = 1/sin(x). Understanding this relationship is crucial for solving trigonometric identities, as it allows for the transformation of expressions involving sine into those involving cosecant.

Trigonometric Identities

Trigonometric identities are equations that hold true for all values of the variable where both sides are defined. Common identities include the Pythagorean identities, reciprocal identities, and co-function identities. Recognizing these identities is essential for simplifying expressions and solving equations in trigonometry.

Reciprocal Identities

Reciprocal identities are a specific set of trigonometric identities that express the relationship between sine, cosine, tangent, and their respective cosecant, secant, and cotangent functions. For example, csc(x) = 1/sin(x) and sec(x) = 1/cos(x). These identities are fundamental for completing expressions and solving trigonometric equations.