Cotangent Function

The cotangent function, written as cot(x) or cotangent(x), is a trigonometric function that represents the ratio of the adjacent side to the opposite side of a right-angled triangle. It is defined as the reciprocal of the tangent function. The cotangent function is used in trigonometry to solve various problems related to angles and sides of triangles.

Definition

The cotangent of an angle in a right-angled triangle is calculated as the ratio of the length of the adjacent side to the length of the opposite side. In terms of the sides of a right-angled triangle with an angle θ, the cotangent function is defined as:

\[ \cot(\theta) = \frac{\text{adjacent side}}{\text{opposite side}} \]

Graph of Cotangent Function

The graph of the cotangent function is a periodic function with vertical asymptotes. It repeats every π radians or 180 degrees. The graph intersects the x-axis at the points where the cotangent function is equal to zero.

Study Guide

Here are some key points to remember when studying the cotangent function:

Understand the definition of the cotangent function as the ratio of the adjacent side to the opposite side in a right-angled triangle.
Learn how to calculate the cotangent of an angle using the given sides of a right-angled triangle.
Study the properties and characteristics of the graph of the cotangent function, including its periodic nature and vertical asymptotes.
Practice solving trigonometric equations and problems involving the cotangent function.
Understand the relationship between the cotangent function and other trigonometric functions, such as sine, cosine, and tangent.

By mastering the cotangent function and its properties, you will develop a strong foundation in trigonometry and be able to solve a wide range of problems related to triangles and angles.