Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

6. Trigonometric Identities and More Equations

Introduction to Trigonometric Identities

Trigonometry

6. Trigonometric Identities and More Equations

Introduction to Trigonometric Identities

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Problem 5.4

Textbook Question

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

Verified step by step guidance

Recall the definition of cotangent: \( \cot x = \frac{1}{\tan x} \).

Use the identity for tangent: \( \tan x = \frac{\sin x}{\cos x} \).

Substitute the expression for \( \tan x \) into the cotangent definition: \( \cot x = \frac{1}{\frac{\sin x}{\cos x}} \).

Simplify the expression: \( \cot x = \frac{\cos x}{\sin x} \).

Recognize that \( \cot x = \frac{\cos x}{\sin x} \) is a fundamental trigonometric identity.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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

Key Concepts

Cotangent Function

Trigonometric Identities

Reciprocal Identities

Watch next

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