i have a bunch of sunrise points, and i have to make a cosine function for it. what assumptions must be made?
To create a cosine function based on a set of sunrise points, certain assumptions need to be made. Here are the key assumptions:
1. Periodicity: It is assumed that the sunrise points repeat in a regular pattern. This means that the time between consecutive sunrise points is constant.
2. Smoothness: The function assumes that the transitions between sunrise points are continuous and smooth. This means that there are no abrupt changes or spikes between the data points.
3. Linearity: The cosine function assumes that the relationship between time and sunrise points is linear over the defined period.
4. Consistency: It is assumed that the observed sunrise points accurately represent the actual sunrise times for the given location and time period.
5. No External Factors: The cosine function assumes that there are no external factors such as weather conditions or seasonal variations affecting the sunrise times.
Once these assumptions are satisfied, you can proceed to create a cosine function that approximates the given set of sunrise points. Remember, data analysis and statistical techniques can help validate these assumptions before constructing the function.