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The sine function for the given scenario is y = 6sin ( (π / 10) x ) - 10.
<u>Step-by-step explanation:</u>
The standard formula for sine function is Asin(Bx)+C.
A buoy bobs up and down 6 meters. That is the buoy shifts vertically and horizontally for 6 meters which is amplitude.
∴Amplitude A= 6.
Period is the distance in the x-axis that makes one full oscillation.
We know that the time taken buoy to move from its highest point to lowest point (half oscillation) is 10 seconds.
∴The period for full oscillation is 20 seconds.
Also, Period =2π divided by B.
⇒ 20 (B) = 2π.
B=2π /20.
= π/ 10.
Since the buoy is in the depth of the ocean 10 meters C = -10.
Applying all the values in the formula,
⇒y = 6sin ( (π/ 10) x ) - 10.
The first point is the mid line,
The first point is x=0,
⇒y=6sin(0)-10.
y= -10.
∴ The line starts at the point y = -10.
The second point is either maximum or minimum value.
That is (5,-4) and (15, -16.)
The answer is:
The explanation for this answer is shown below:
1. By definition, the amount of second required for the pendulum to move from its resting position and return, is the period.
2. As you can see in the graph attached in the exercise, the wave interval is repeating every two units of x (or ).
3. Therefore, the period is .