Question
What is the amplitude of \( y=\sin (x) ? \)
Ask by Mullins Parsons. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The amplitude of \( y = \sin(x) \) is 1.
Solution
The amplitude of a sine function, such as \( y = \sin(x) \), is the maximum value that the function reaches from its midline (which is typically the x-axis for the sine function).
For the function \( y = \sin(x) \):
- The sine function oscillates between -1 and 1.
- Therefore, the amplitude \( A \) is calculated as:
\[
A = \frac{\text{Maximum value} - \text{Minimum value}}{2}
\]
In this case:
- Maximum value = 1
- Minimum value = -1
Now, substituting these values into the amplitude formula:
\[
A = \frac{1 - (-1)}{2} = \frac{1 + 1}{2} = \frac{2}{2} = 1
\]
Thus, the amplitude of \( y = \sin(x) \) is \( 1 \).
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Simplify this solution The Deep Dive
The amplitude of the function \( y = \sin(x) \) is 1. This means that the maximum value of the sine wave reaches 1 and the minimum value dips down to -1, oscillating perfectly between these two values. So, whenever you're riding the wave of sine, know that it likes to stay within this sweet range! Understanding amplitude can be super handy in real-world situations, like sound waves and light waves! For instance, in sound, the amplitude determines how loud a sound is—greater amplitude means a louder sound. So next time you're blasting your favorite tunes or enjoying nature's symphony, you can appreciate how amplitude brings those sounds to life!
