If n is an integer, n • 180° represents an integer multiple of 180°, (2n + 1) • 90° represents an odd integer multiple of 90° , and so on. Determine whether each expression is equal to 0, 1, or ―1, or is undefined. cot[n • 180°]

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). The cotangent function is periodic with a period of π (or 180°), meaning that cot(x + kπ) = cot(x) for any integer k. Understanding this periodicity is crucial for evaluating cotangent at specific angles.

Integer Multiples of Angles

When we refer to integer multiples of an angle, such as n • 180°, we are discussing angles that can be expressed as k times a base angle, where k is an integer. For example, n • 180° can take values like 0°, 180°, 360°, etc. This concept is important for determining the values of trigonometric functions at these specific angles, particularly since cotangent is undefined at odd multiples of 90°.

Trigonometric Values at Key Angles

Trigonometric functions have specific values at key angles, such as 0°, 90°, 180°, and 270°. For instance, cot(0°) = undefined, cot(90°) = 0, and cot(180°) = undefined. Recognizing these values helps in evaluating expressions involving cotangent, especially when the angle is expressed as an integer multiple of 180°.