Question

The propeller of a boat at dock in the ocean will rise and fall with the waves. On a particularly wavy night, the propeller leaves its resting position and reaches a height of 2m on the peaks of the waves and -2m in the troughs. The time between the peak and the trough is approximately 3 seconds. Determine the equation of a sinusoidal function that would model this situation assuming that at equation , the propeller is at its resting position and headed towards the peak of the next wave.

Answer 1

The base sin function (f(x) = sin(x)) has an amplitude of 1 (peak up to 1 and trough down to -1); since this propeller reaches a maximum peak of 2 and a minimum trough of -2, we will multiply the amplitude by 2.
Normally, the distance between a peak and a trough is equal to pi, but we want this value to be 3; so, we multiply the frequency by pi and divide by 3.
When these transformations are applied to the equation, we get the end result:

f(x) = __*sin(__*x)

The outside blank corresponds to the amplitude (remember, we want to multiply this by 2); and the inner blank corresponds to the frequency (we want to multiply this by pi and divide it by 3)
Can you fill in the blanks to get the equation needed to represent this wave?

Answer 2

thank you

Answer 3

so this is how u do it but what where is the work??

Answer 4

so the equation is f(x) = __*sin(__*x) ?

Answer 5

uuh

Answer 6

no it is all god thank you