Functions in physics

1. Give a physical example related to the sine or cosine function and sketch it's graph.

2. Give the Analytical or mathematical expression using physical quantities and explain all the abbreviations used.

3. Find the derivative or integral of the functions (the one which is physically more meaningful) What function is the derivative or integral and in which limit is the derivative or integral changing (initial and final values)? Explain which physical quantity is the derivative or integral.

4. What is the property of the nature or the model describing it, which causes exactly such kind of functional dependence between physical qualities (the one described by the graph)