For the given periodic funntion a) the amplitude b) the period – Free B14
For the given periodic funntion a) the amplitude b) the period
Answer
📈 Amplitude and Period of a Periodic Function
🔹 Understanding Periodic Functions
A periodic function repeats its values at regular intervals along the x-axis. Examples include sine and cosine functions.
- Amplitude: Measures how tall the wave is from the centerline to a peak or trough.
- Period: Measures the horizontal length of one full cycle of the function.
🔸 Part (a): Finding the Amplitude
The amplitude is half the vertical distance between the wave’s maximum and minimum values.
Amplitude = (Maximum − Minimum) / 2
From the graph:
- Maximum value = 3
- Minimum value = −3
Amplitude = (3 − (−3)) / 2 = 6 / 2 = 3
Answer (a): Amplitude = 3
🔸 Part (b): Finding the Period
The period is the distance between two identical points in the wave’s cycle along the x-axis.
- First peak occurs at x = −4
- Next peak occurs at x = 4
Period = xfinal − xinitial = 4 − (−4) = 8
Answer (b): Period = 8
📘 Summary
| Property | Value |
|---|---|
| Amplitude | 3 |
| Period | 8 |
🧠 Insight
These values are essential in defining trigonometric functions such as:
f(x) = A · sin(2πx / T) or A · cos(2πx / T)
Where:
A = Amplitude = 3
T = Period = 8