Question

sketch a graph and write an equation for a sinusoidal function that has a period of 12 seconds, a maximim height of 8ft and a minimim height of -4 ft. At a time t=0, the function's height is at its highest point.

Answer 1

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Answer:

see attached

Explanation:

The amplitude of the function is half the difference between the maximum and minimum:

A = (8 -(-4))/2 = 6

The multiplier of t is (2π)/period, so is ...

B = (2π)/12 = π/6

The vertical offset is the average of the minimum and the maximum:

D = (8 +(-4))/2 = 2

The peak is at t=0, so the cosine function is the appropriate choice.

__

Then the function is ...

f(t) = Acos(Bt) +D

f(t) = 6cos(πt/6) +2