Understanding Amplitude, Period, and Midline
The function in question is y = 7 sin(4x) + 2. Let’s break it down to identify its amplitude, period, and midline.
Amplitude
The amplitude of a sine function is determined by the coefficient in front of the sine function. In this case, the function has a coefficient of 7 in front of sin(4x). This means:
- Amplitude: 7
Thus, the function oscillates between 7 and -7, giving it a total height of 14 units from peak to trough.
Period
The period of a sine function is calculated using the formula:
Period = 2π / |b|
In our function, b is the coefficient of x inside the sine function, which is 4. Plugging this into the formula gives us:
- Period: 2π / 4 = π / 2
This means the function will complete one full cycle every π/2 units along the x-axis.
Midline
The midline of a sine function is the horizontal line that runs through the middle of the function’s oscillation. It is determined by the constant added to the sine function. In this case, we see:
- Midline: 2
This indicates that the sine wave oscillates around the line y = 2.
Summary
To summarize:
- Amplitude: 7
- Period: π/2
- Midline: y = 2