1.10

1.10

1) Main Points

Periodic means repeating at regular intervals. Amplitude is half the distances between the max and min. The period is the time for the function to complete one whole cycle. y=sin(t), the period of a sine function is 2 pi. The number that multiplies the sin(t) part of the function affects the amplitude. If a number is added or subtracted to sin(t) it is shifted up or down accordingly. If a number is added to t then the graph is shifted left, subtracted it is shifted right. Period = 2pi/B and B is the number that will multiply t (y=Asin(Bt).

2) Challenges

1 cycle is when the function goes down then up then back to the starting point. It will be important for me to keep in mind what a whole cycle looks like. It is counter intuitive that when you add a number to t the graph shifts to the negative direction. I will also have to make sure i recognize that this relationship is backward. I will also need to burn into my memory period= 2pi/B. This is a very important for finding the relationship between the parameter B and the period, which are NOT the same.

3) Reflections

Periodic functions are very applicable to the real world. I can imagine using them to describe temperature/whether patterns, tides, or changes in the stock market. So many things occur periodically in the world and a knowledge in periodical functions can help describe them.