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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.)
