Modeling with periodic functions 2

The  exercise appears under the Trigonometry Math Mission, Differential calculus Math Mission and Integral calculus Math Mission. This exercise uses sine and cosine functions to model real-life situations.

Types of Problems
There is one type of problem in this exercise:


 * 1) Write a model for the situation: This problem describes a real-life situation that can be modeled with a sinusoid. The student is asked to find a model for the situation and write it in the space provided.Mwpf2-1.png

Strategies
Knowledge of trigonometric functions and their graphs are important to completing this exercise accurately.
 * 1) The problem will accept either a sine or cosine model, do not worry about using the "incorrect" one.
 * 2) Be careful with the independent variable, often on these problems it is t because the models have time as an independent variable.
 * 3) Getting in a regular order can assist timing, recommended order would be amplitude, horizontal (phase) shift and then period changer. Finally, the vertical shift.
 * 4) Numbers and coefficients do not need to be reduced or simplified for credit.

Real-life Applications

 * 1) Periodic models, often sinusoids are used in earth science to represent hours of daylight, average daily temperature, or tides.
 * 2) In health, the EKG for measuring heart activity appears as a periodic model.
 * 3) Sound waves in music can be represented by periodic models.