Modeling Data With Trigonometric Functions
October 18, 2011
Real-life math is used in many activities that people do in a daily basis. In the next few paragraphs I will be explaining how to use a real world data and model it with a sine function of the form of y= a sin K (x-b). The graphs will use the law of sine which is defines as, “a law stating that the ratio of the sine of an arc of a spherical triangle to the sine of the opposite angle is the same for all three arcs.” The following table gives the number of hours of daylight in Philadelphia, Pennsylvania.
Day | | Mar 21 | Apr 21 | May 21 | | June 21 | | July 21 | | Aug 21 | | Sept 21 | | Oct 21 | | Nov 21 | | Dec 21 | Hours of Day-light | | 12 | 13.7 | 14.2 | | 14.8 | | 14.2 | | 13.7 | | 12 | | 11.4| | 9.8 | | 9.2 |
While plotting the data, I realized that the sine function works better because the graph begins from the point (0) on the x-axis of the graph. Firstly, I realized I need to be able to find my equation before formulating a graph. My equation is y= a sin K (x-b). I need to find the “a”, which stands for amplitude, “the maximum extent of a vibration or oscillation, measured from the position of equilibrium.” I took the difference between the highest and lowest daylight hours reading in the table and divided by two.
14.8 – 9.2 = 5.6/2
Secondly, I figured the period which is defined as, “a space of time between two events or a portion of time.” The formula is 2 /K
2 /k = 365
k = 2 /365
P= 2 /365
Thirdly, the phase shift “represents the amount a wave has shifted horizontally from the original wave.” I was able to figure the phase shift by the information given which stated that, “the time to be in days. March 21 is the 80th day of the year.” With that given I just took the number before what was given equaling it to 79. Our phase shift stands for b in our formula.
B = 79...