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
π Amplitude and Period of a Periodic Function
πΉ 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.
πΈ Part (a): Finding the Amplitude
The amplitude is half the vertical distance between the waveβs maximum and minimum values.
Amplitude = (Maximum β Minimum) / 2
From the graph:
- Maximum value = 3
- Minimum value = β3
Amplitude = (3 β (β3)) / 2 = 6 / 2 = 3
Answer (a): Amplitude = 3
πΈ Part (b): Finding the Period
The period is the distance between two identical points in the waveβs cycle along the x-axis.
- First peak occurs at x = β4
- Next peak occurs at x = 4
Period = xfinal β xinitial = 4 β (β4) = 8
Answer (b): Period = 8
π Summary
| Property | Value |
|---|---|
| Amplitude | 3 |
| Period | 8 |
π§ Insight
These values are essential in defining trigonometric functions such as:
f(x) = A Β· sin(2Οx / T) or A Β· cos(2Οx / T)
Where:
A = Amplitude = 3
T = Period = 8