To find the points where g(t) is equal to the average sea level (which is 0), we can set the equation equal to 0 and solve for t:
0 = 4sin(π/6t)
To solve for t, we can take the inverse sine (or arcsine) of both sides:
sin^(-1)(0) = sin^(-1)(4sin(π/6t))
Since sin^(-1)(0) = 0 (in the interval [0, 2π]), we have:
0 = π/6t
To isolate t, we can multiply both sides by 6/π:
0 = t
Therefore, the points where g(t) is equal to the average sea level are when t = 0.
Use the drawing tools to form the correct answer on the graph.
Every day the ocean has two low tides and two high tides. Function g represents the height, in feet, of the water level in a cove relative to the average sea level. Let t represent the number of hours elapsed since the water height was equal to the average sea level after a low tide.
g(t)\:=\:4\sin\left ( \frac{\pi}{6}t \right )
Plot the points where g(t) is equal to the average sea level.
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