The CHEERS project is attempting to determine how far two roller coasters need to be pushed in order to overlap regions that are each half the size of one of the coasters. Without using any built-in trigonometric functions or mathematical constants, like pi, the answer must be discovered. Other than simple input, output, and arithmetic operations, it is also not permitted to use any external programming tools. Calculations in geometry and algebra were employed to address the issue. These calculations assisted in determining the required separation between the two coasters. These calculations were used to identify a remedy to the issue. This solution can serve as a starting point for more field study.

Assumptions

• To calculate the value of α, we have used Newton-Raphson method where we initialized α at π/2.

• In the Newton-Raphson method, we also have assumed tolerance to be 1e-6.

• To calculate sin(x) and cos(x) in our program we have used Taylor series with n (default = 10) elements.

• We assumed that for this first deliverable iteration, it was not necessary for the user to choose the number of iterations for the estimating functions.

Instructions to process the source code:

• For Incarnation 1, run the main.py file from incarnation1 folder and to execute the Incarnation 2, use the main.py from incarnation 2 folder using any python 3.10 or above environment.

• To run it on local system use the main.py file and run it on command prompt.