Maximum and Minimum Values of Sin(x)

📌 CONCEPT: The sine function y = sin(x) is a periodic trigonometric function that oscillates between its maximum and minimum values, with an amplitude of 1 and a period of 2π.

📐 RULE / FORMULA: The maximum value of the sine function is 1, and the minimum value is -1, which can be determined using the unit circle or the properties of the sine function.

💡 WORKED EXAMPLE: To determine the maximum and minimum values of the function y = sin(x), consider the unit circle. At x = π/2, the function reaches its maximum value, 1. Similarly, at x = 3π/2, the function reaches its minimum value, -1.

⚠️ COMMON MISTAKE: Students often confuse the amplitude and the period of the sine function. The amplitude is the maximum value of the function, which is 1 for the sine function, whereas the period is the distance between two consecutive maxima or minima, which is 2π for the sine function.