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

Verified step by step guidance

1. Recall the definition of cotangent: \( \cot x = \frac{1}{\tan x} \).
2. Use the identity for tangent: \( \tan x = \frac{\sin x}{\cos x} \).
3. Substitute the expression for \( \tan x \) into the cotangent definition: \( \cot x = \frac{1}{\frac{\sin x}{\cos x}} \).
4. Simplify the expression: \( \cot x = \frac{\cos x}{\sin x} \).
5. Recognize that \( \cot x = \frac{\cos x}{\sin x} \) is a fundamental trigonometric identity.

Key Concepts

Cotangent Function

The cotangent function, denoted as cot(x), is the reciprocal of the tangent function. It is defined as cot(x) = cos(x)/sin(x). Understanding cotangent is essential for solving trigonometric identities, as it relates to the sine and cosine functions, which are fundamental in trigonometry.

Trigonometric Identities

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. Common identities include the Pythagorean identities, reciprocal identities, and co-function identities. Recognizing these identities is crucial for simplifying expressions and solving equations in trigonometry.

Reciprocal Identities

Reciprocal identities express the relationships between trigonometric functions and their reciprocals. For example, the reciprocal identity for cotangent states that cot(x) = 1/tan(x). These identities are vital for transforming and manipulating trigonometric expressions to complete identities or solve equations.