Perform each transformation. See Example 2.
Write cot x in terms of sin x.

Verified step by step guidance

1. Recall the definition of cotangent: \( \cot x = \frac{1}{\tan x} \).
2. Express tangent in terms of sine and cosine: \( \tan x = \frac{\sin x}{\cos x} \).
3. Substitute the expression for tangent into the cotangent formula: \( \cot x = \frac{1}{\frac{\sin x}{\cos x}} \).
4. Simplify the expression by taking the reciprocal: \( \cot x = \frac{\cos x}{\sin x} \).
5. Now, \( \cot x \) is expressed in terms of \( \sin x \) and \( \cos x \).

Key Concepts

Cotangent Function

The cotangent function, denoted as cot(x), is the reciprocal of the tangent function. It can be expressed as cot(x) = cos(x) / sin(x). Understanding cotangent is essential for transforming trigonometric expressions, as it relates directly to sine and cosine functions.

Sine Function

The sine function, denoted as sin(x), is a fundamental trigonometric function that represents the ratio of the length of the opposite side to the hypotenuse in a right triangle. It is crucial for expressing other trigonometric functions, including cotangent, in terms of sine.

Trigonometric Identities

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. They are essential tools for transforming and simplifying trigonometric expressions, such as expressing cotangent in terms of sine, which relies on these established relationships.