Trigonometry mountain assessment problem

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SUMMARY

The forum discussion centers on calculating the equation of a sinusoidal roller coaster track based on given dimensions. The high and low points of the track are separated horizontally by 50 meters and vertically by 30 meters, with the low point positioned 3 meters below ground level. The equation to express the height of the track, y, in terms of the horizontal distance, x, is suggested to be in the form of y = a sin(bx + c) + d, where specific values for a, b, c, and d need to be determined based on the problem's parameters.

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  • Familiarity with trigonometric equations
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  • Knowledge of horizontal and vertical shifts in functions
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A portion of a roller coaster track is to built in the shape of a sinusoid. You have been hired to calculate the lengths of the horizontal and vertical timber supports to be used. The high and low points on the track are separated by 50 meters horizontally and by 30 meters vertically. The low point is 3 meters below ground. Let y be the number of meters the track is above the ground and x be the number of meters horizontally from the high point, write an equation expressing y in terms of x.
 
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Hello and welcome to MHB, jenherting! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 
So far the work that I have was I drew a sketch of the graph itself and now I just need help on how to write the equation and what parts of the problem represents the aspects of a sinusoidal equation.
 
jenherting said:
The low point is 3 meters below ground.

This seems odd. Are you sure it's not 3 meters above the ground?

You need an equation of the form

$$y=a\sin(bx+c)+d$$

Any thoughts on where to begin?
 

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