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. cos[n • 360°]

Key Concepts

Periodic Functions

Trigonometric functions like cosine are periodic, meaning they repeat their values in regular intervals. For cosine, the period is 360°, so cos(θ) = cos(θ + 360°k) for any integer k. This property allows us to simplify expressions involving angles that are multiples of 360°.

Cosine Function Values

The cosine function outputs specific values for key angles. For example, cos(0°) = 1, cos(180°) = -1, and cos(360°) = 1. Understanding these values is crucial for evaluating expressions involving cosine, especially when the angle is expressed in terms of multiples of 360°.

Integer Multiples of Angles

When an angle is expressed as an integer multiple of a base angle, such as n • 360°, it indicates that the angle can be simplified based on the periodic nature of trigonometric functions. For any integer n, cos(n • 360°) will always equal cos(0°), which is 1, due to the periodicity of the cosine function.