A wooden roller coaster contains a run in the shape of a sinusoidal curve, with a series of hills. The crest of each hill is 108 feet above the ground. If it takes a car 1.9 seconds to go from the top of a hill to the bottom (4 feet off the ground), find a sinusoidal function of the form y = A sin(ωt - Φ) + B that models the motion of the coaster train during this run starting at the top of a hill.

Step-by-step explanation:

We are given that

Height of crest, h=108 feet

Time for one cycle, T=1.9 s

We have to find a sinusoidal function of the form y = A sin(ωt - Φ) + B that models the motion of the coaster train during this run starting at the top of a hill.

We are given

Amplitude,

Using the formula

We assume,

Horizontal shift

Substitute the values

Hence, the  sinusoidal function  that models the motion of the coaster train during this run starting at the top of a hill is given by

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you first to choose the points and then move from then as the slope you have