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. sin[270° + n • 360°]

Key Concepts

Periodic Functions

Trigonometric functions like sine and cosine are periodic, meaning they repeat their values in regular intervals. For sine, the period is 360°, so sin(θ) = sin(θ + 360°k) for any integer k. This property allows us to simplify expressions involving angles by reducing them to their equivalent angles within one full cycle.

Sine Function Values

The sine function has specific values at key angles, such as sin(0°) = 0, sin(90°) = 1, sin(180°) = 0, and sin(270°) = -1. Understanding these values is crucial for evaluating sine expressions, especially when combined with periodicity, as it helps determine the output of the sine function for any angle.

Angle Addition

The angle addition formula for sine states that sin(a + b) = sin(a)cos(b) + cos(a)sin(b). In this context, we can analyze sin(270° + n • 360°) by recognizing that adding multiples of 360° does not change the sine value, allowing us to focus on sin(270°) directly, which simplifies the evaluation.