Trigonometry mountain assessment problem

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Discussion Overview

The discussion revolves around a problem involving the design of a roller coaster track shaped like a sinusoid. Participants are exploring how to formulate an equation that represents the height of the track above ground in relation to its horizontal position, based on given measurements of vertical and horizontal distances between high and low points.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant describes the problem, specifying the horizontal and vertical distances between the high and low points of the track.
  • Another participant requests that the original poster share their progress to facilitate better assistance.
  • A participant mentions having drawn a sketch of the graph and seeks help in writing the sinusoidal equation and understanding its components.
  • There is a challenge regarding the stated low point being 3 meters below ground, with a participant questioning if it should instead be above ground.
  • A suggestion is made to use the general form of a sinusoidal equation, prompting further thoughts on how to start the formulation.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the specifics of the equation or the interpretation of the low point's height. Multiple viewpoints and uncertainties remain regarding the correct formulation and understanding of the problem.

Contextual Notes

There are unresolved aspects regarding the interpretation of the low point's height and how it affects the equation. The discussion also lacks specific mathematical steps or assumptions that may be necessary for deriving the equation.

jenherting
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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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