Modeling with periodic functions

The  exercise appears under the Trigonometry Math Mission. This exercise strengthens understanding of trigonometric functions by using them to model periodic behavior.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the requested information from the model: This problem provides a model for a real-life situation. The student is asked to find the answer to a piece of information about the trigonometric function.Mwpf1.png
 * 2) Write the model and use it to answer a question: This problem describes a situation that can be modeled with a periodic function. The student is asked to find the model for the situation, and then use it to answer a related question.Mwpf2.png

Strategies
Knowledge of the parent functions for sine and cosine and the functional transformations are encouraged to ensure success on this exercise.
 * 1) The general form of a trig function is $$Atrig(B(x-C))+D $$.
 * 2) A is the amplitude of the trig function.
 * 3) B is the horizontal scale factor, and the period is $$\frac{2\pi}{B}$$.
 * 4) C is the horizontal shift
 * 5) D is the vertical shift
 * 6) The problems in this exercise do not seem to have horizontal or vertical shifts.

Real-life Applications

 * 1) The problems in this exercise are applications.
 * 2) Sinusoids are used to model periodic behavior, such as the number of hours of daylight, or temperature cycles over a day, or a year.
 * 3) Light and sound travel in waves that are shaped like sine and cosine curves.