HELP I HAVE A TEST TMR MORNING!!!!!!
A boat tied up at a dock bobs up and down with passing waves. The vertical distance between its high point and its low point is 1.8m and the cycle is repeated every 4 s.
Here is the equation that models this: [tex]f(x)=0.9sin(\frac{\pi }{2} x)[/tex]
^The y-coordinates are in m and the x coordinates is the time in seconds

b) Use the model to determine when, during each cycle, the boat is 0.5m above the mean positition.

BRAINLIEST!!!!

The time the boat is 0.5 m above the mean position during each cycle is (4n + 0.375) s

Since y = f(x) = 0.9sin(πx/2)

We want to determine the time, x at which the boat is 0.5 m above its mean position. This is the value of y at y = 0.5 m

So, y = f(x) = 0.9sin(πx/2)

0.5 = 0.9sin(πx/2)

Dividing through by 0.9, we have

0.5/0.9 = sin(πx/2)

5/9 = sin(πx/2)

Taking inverse sine of both sides, we have

sin⁻¹(5/9) = πx/2

sin⁻¹(0.5556) = πx/2

0.589 rad = πx/2

x = 2 × 0.589/π

x = 1.178/π

x  = 0.375 s

Since the boat repeats its cycle every 4 seconds, the time the boat is 0.5 m above the mean position after n cycles is t = (4n + 0.375) swhere n is a positive integer. That is n = 0, 1, 2, 3...

So, the time the boat is 0.5 m above the mean position during each cycle is (4n + 0.375) s

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