The water level in a lake rises to a maximum of 4m above sea level and drops to a minimum of 6m below sea level in a periodic table. A maximum height occurs every 8 hours. If it is currently at its maximum height at 6am determine a sine and cosine function that determines the height of the water, h, in meters, after each hour, t.

Given that the water level in the lake rises to a maximum of 4m above sea level and drops to a minimum of 6m below sea level, the amplitude of the sine and cosine functions will be \frac{4 + 6}{2} = 5 meters. The average value of the water level will be at sea level.

The period of the function is 8 hours since the maximum height occurs every 8 hours.

Since the water level is currently at its maximum height at 6 am, we can let the maximum point be at t = 0.

The general form of a sine function is h(t) = A \sin(Bt - C) + D, where:
- A is the amplitude,
- B is the period,
- C is the phase shift,
- D is the vertical shift.

Similarly, the general form of a cosine function is h(t) = A \cos(Bt - C) + D.

With the given information, the sine function that represents the height of the water level, h(t), after each hour, t, is:
h(t) = 5\sin\left(\frac{\pi}{4}t\right) + 0

And the cosine function is:
h(t) = 5\cos\left(\frac{\pi}{4}t\right) + 0

\boxed{h(t) = 5\sin\left(\frac{\pi}{4}t}\) Answer.

\boxed{h(t) = 5\cos\left(\frac{\pi}{4}t}\) Answer.