What is the amplitude of y = sin x?

Question

Explain how you know

Answer 1

The amplitude of the function \( y = \sin x \) is 1.

Amplitude is defined as the maximum distance from the midline of a periodic function to its peak or trough. In the case of the sine function:

1. The sine function oscillates between -1 and 1.
2. The midline of the sine function is at \( y = 0 \).
3. The maximum value (peak) of \( y = \sin x \) is 1, and the minimum value (trough) is -1.

To find the amplitude, we take the absolute value of the maximum value (since amplitude is always a non-negative quantity):

\[ \text{Amplitude} = \frac{\text{Maximum value} - \text{Minimum value}}{2} = \frac{1 - (-1)}{2} = \frac{2}{2} = 1. \]

Thus, the amplitude of \( y = \sin x \) is 1.