EXCEL 1.1
To create this spreadsheet, I developed a mathematical model that represents a sine wave based on its fundamental components. The objective was to break down the function $Y(T) = A \cdot \sin(W \cdot T + \phi)$ to understand how each variable affects the final result.
1. Definition of Control Variables
At the top of the sheet, I have set up a section for configurable parameters. These values act as the constants of the function:
W (Angular Frequency): Set at 100, it determines the periodicity of the wave.
Ø (Initial Phase): Defined at 32.3 degrees, it marks the starting point of the cycle.
A (Amplitude): With a value of 311, it defines the maximum and minimum height of the wave.
By placing these variables independently, the model is dynamic; any change in these cells automatically updates all calculations and the graph.
2. Development of the Data Table
The main table was designed to perform the calculations sequentially to avoid syntax errors in the formulas:
Column T (Time): I entered time values distributed between 0 and 6. The choice of non-equally spaced values allows us to observe how the scatter plot interprets the data independently of its order.
Calculation of the Argument (WT and WT+ø): In the first columns, I calculated the product of the frequency and time and added the initial phase. These calculations were originally performed in sexagesimal degrees.
Conversion to Radians: Since trigonometric functions in spreadsheets operate in radians by default, I applied the
RADIANSfunction to the previous column. This is a critical step to ensure a correct mathematical representation.Calculation of the Y(T) Function: After obtaining the sine of the argument, I multiplied the result by the amplitude A. This scales the wave to the desired values.
3. Graphical Representation
Finally, I generated a Scatter Plot using the data from column T for the x-axis and column Y(T) for the y-axis. The result is a clear visualization of the points that form the wave, allowing for visual verification that the function's behavior matches the expected results based on the input parameters.
To make the document easier to read, I applied cell styles and formatting to clearly distinguish the data entry zones from the calculation and result areas.






