A theme park guest takes an innertube into the wave pool. The innertube moves up and down in a way such that the height h of the innertube, in meters, above the floor of the pool can be modeled by the function h = asinbx + 5. When the wave pool is turned on, the innertube's height fluctuates between 2 meters and 8 meters, with an interval of 12 seconds between maximums. Based on the context of the problem, what are the values of a and b?

a = 3 and b equals pi over 12
a = 3 and b equals pi over 6
a = 6 and b equals pi over 12
a = 6 and b equals pi over 6

It is defined as a function which is sinusoidal in nature, and it has a domain of all real numbers and lies between the [a, a] where is a amplitude of the function.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

As we know,

-1 ≤ sinx ≤ 1

-a + 5 = 2

a = 3

12 = 2π/b

b = π/6

Thus, the value of a = 3 and b = π/6 if the innertube's height fluctuates between 2 meters and 8 meters option second is correct.

Learn more about the sin function here:

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